How to Solve Matrix Reasoning Questions, Step by Step
To solve matrix reasoning questions, read the grid one row at a time and ask what changes from left to right, then check the columns to confirm, then name the rule before you look at the answer choices. Most matrix items use one of five rules: something stays the same, something changes steadily, three values are spread across the row, shapes are added or subtracted, or a hidden feature changes. Use the rule to rule out wrong answers, and the right one is usually what's left.
If matrix puzzles make you freeze or guess, IQ Tester finds out whether the slip is pattern spotting, working memory or scattered attention, and trains that one: Find my weak spots.
What a matrix item is
A matrix reasoning question shows a grid of pictures, usually 3×3, with the bottom-right cell missing. Below it are six or eight answer options. You pick the one that completes the pattern.
That's the whole format. There are no words and no math, which is why matrix reasoning tests are used as a "non-verbal" measure of reasoning. Matrix Reasoning is a named subtest on the Wechsler scales, the WISC for children and the WAIS for adults, and Raven's Progressive Matrices is a whole test built from these items.
What makes them hard isn't the pictures. It's that several features can change at once: shape, size, number, shading, position and rotation. Your job is to untangle which features follow which rule.
The two-second setup
Before anything else, glance at the grid and name the features you see. For example: "Circles and squares. Some are black. The count changes." That quick scan tells you what to track.
Read rows, then columns
Here's the core method for how to solve matrix reasoning problems.
- Cover the answers. If you look at them first, you'll start matching pictures instead of finding the rule.
- Read row 1, left to right. What changes from cell 1 to cell 2 to cell 3? Say it in words.
- Read row 2 the same way. Does the same rule hold? If yes, you've probably got it.
- Check the columns. Sometimes the rule runs top to bottom instead, or both ways.
- Apply the rule to row 3 and picture what the missing cell must look like.
- Now look at the answers and find the one that matches your prediction.
Rows first, because most test-makers build items so that each row follows the rule. Columns are your check.
The five common rules
Researchers who studied Raven's matrices in detail found that items are built from a small set of rule types. You don't need the research to use them. Just learn to spot these five. (For the Raven's-specific version, see how to solve Raven's Progressive Matrices.)
| Rule | What you see in a row | Example |
|---|---|---|
| Constant | A feature stays the same across the row | All three shapes are triangles |
| Steady change | A feature grows or shrinks by a step | 1 dot, 2 dots, 3 dots |
| Three values spread | Three versions appear once each per row | Circle, square, star in every row, in a new order |
| Add or subtract | Cell 3 = cell 1 + cell 2 (or minus) | Lines in cell 1 plus lines in cell 2 make cell 3 |
| Hidden feature | A less obvious property follows the rule | Shading, rotation or position shifts |
Rule 1: constant
The easiest one. If every cell in a row has a black shape, the missing cell will too. Constants often run alongside a harder rule, so don't stop once you've found one.
Rule 2: steady change
Something increases or decreases by the same amount: size, number of items, angle of rotation. If row 1 goes 1, 2, 3 dots and row 2 goes 2, 3, 4 dots, row 3 probably goes 3, 4, 5.
Rule 3: three values spread
Each row contains the same three things, just shuffled. If rows 1 and 2 each have one circle, one square and one star, and row 3 has a star and a circle, the missing one is a square. This rule is very common and easy to miss because nothing seems to "change."
Rule 4: add or subtract
Overlay the first two cells. Does the third cell show everything combined? Or only the lines that appear in one but not both? Test it on row 1 before assuming.
Rule 5: hidden features
When the obvious features don't explain the row, look closer: which way are shapes pointing? Where in the cell do they sit? Is the shading moving? These are the features that separate easy items from hard ones.
This is where matrix puzzles get tricky on your own: you're tracking three or four features at once, and it's hard to know whether you missed a rule because you didn't see it or because you lost track of it. IQ Tester's 16 questions tell pattern spotting apart from working memory and scattered attention, then give you a short daily drill for your actual weak spot. Find my weak spots
Eliminate wrong answers
Even when you can't fully work out the rule, elimination gets you a long way.
Answer options in matrix tests are often built to be nearly right. Each wrong answer usually breaks one rule. So:
- Check one feature at a time. If you know the missing shape must be black, cross out every white option.
- Then check the next feature. If it must have three dots, cross out the rest.
- Keep going until one is left. Often you'll get there before you've found every rule.
This is the single best tip for matrix reasoning tests: you don't have to solve the whole puzzle if you can rule out five of six options.
Common traps
- An option that copies a cell from the grid exactly. It's rarely correct.
- An option that's right in shape but wrong in count.
- An option that's a mirror image of the right answer.
Worked matrix reasoning examples
These are described in words so you can follow along.
Example 1: steady change plus constant
- Row 1: one small circle, two small circles, three small circles
- Row 2: one small square, two small squares, three small squares
- Row 3: one small triangle, two small triangles, ?
Rule: shape is constant in each row, count goes up by one. Answer: three small triangles.
Example 2: three values spread
- Row 1: black circle, grey square, white star
- Row 2: grey star, white circle, black square
- Row 3: white square, black star, ?
Each row has one of each shape and one of each shading. Row 3 is missing a circle, and it's missing grey. Answer: grey circle.
Example 3: add
- Row 1: a vertical line, a horizontal line, a cross (both lines)
- Row 2: a diagonal line, the other diagonal, an X
- Row 3: a circle, a dot in the center, ?
Cell 3 is cells 1 and 2 overlaid. Answer: a circle with a dot in the center.
Example 4: hidden rotation
- Row 1: an arrow pointing up, right, down
- Row 2: an arrow pointing right, down, left
- Row 3: an arrow pointing down, left, ?
Each step turns the arrow 90° clockwise. Answer: arrow pointing up.
Daily practice: how to improve matrix reasoning
Matrix reasoning improves with the same kind of practice as any skill: short sessions, clear feedback and focusing on what you get wrong.
A simple routine:
- Do three to five items a day, not fifty once a week.
- Say the rule out loud before checking the answer. If you can't say it, you haven't found it.
- Keep a miss log. Write which rule type you missed. After a week, you'll see a pattern, like "I always miss three-values-spread."
- Practice that rule type on purpose.
- Time yourself only after you're accurate. Speed comes second.
If you enjoy shape puzzles, the SCANS checklist in how to answer abstract reasoning tests is another handy tool for the same kind of item.
Know which matrix rule you keep missing
You now know how to solve matrix reasoning: rows first, name the rule, check the five common types, then eliminate. The hard part is seeing your own pattern of mistakes. IQ Tester takes about two minutes, gives you a reasoning tier and pins down your weak spots, then sets one tip and one 10-minute drill a day, weighted toward them, with a streak and history so you can watch it change.
FAQ
What is matrix reasoning?
Matrix reasoning is a type of non-verbal reasoning question where you see a grid of patterns with one cell missing and choose the option that completes it. It tests your ability to spot rules in visual information. It's a subtest on the Wechsler scales and the basis of Raven's Progressive Matrices.
What does the WISC matrix reasoning subtest involve?
On the WISC, a child looks at an incomplete matrix or series of pictures and picks the option that completes it. It's one of the subtests used to look at fluid reasoning. Scoring and interpretation are done by a trained psychologist, not by practice sites.
How can I get better at matrix reasoning puzzles?
Practice a few items every day, say the rule out loud before you check, and keep a log of which rule types you miss. Then focus on those types. Short, regular practice with feedback beats long random sessions.
What are the most common matrix reasoning tricks?
Cover the answers first, read rows before columns, and use elimination one feature at a time. Watch for the "three values spread" rule, where each row contains the same three items in a different order, because it's easy to overlook.
Is there a free matrix reasoning test practice?
Many sites offer sample matrix puzzles to try. For practice aimed at your own weak spots, IQ Tester includes pattern drills in its daily 10-minute session; you sign in with Google and pay once rather than subscribe.