Quick start
- Choose 2x2 or 3x3.
- Choose the operation you want.
- Enter Matrix A. Enter Matrix B too for add, subtract, and multiply.
- Press Calculate matrix, then check the result, steps, examples, and recent answers.
Best uses
Use this page when the problem is about small square matrices and you want to check the answer without losing the row and column logic.
- Check 2x2 and 3x3 matrix addition or subtraction before homework goes in.
- Multiply square matrices and see the row-by-column rule instead of just the answer.
- Find a 2x2 determinant with ad - bc or a 3x3 determinant with expansion by minors.
- Transpose a matrix when rows and columns need to switch places.
Fast 2x2 checks
For addition, match the same position in each matrix. [[1,2],[3,4]] plus [[5,6],[7,8]] becomes [[6,8],[10,12]]. Nothing moves around.
For a 2x2 determinant, use ad - bc. Matrix [[3,4],[2,5]] gives 3x5 - 4x2 = 7. If you get a different number, check the diagonal order first.
Matrix multiplication order
Matrix multiplication uses rows from Matrix A and columns from Matrix B. That is why A x B can be different from B x A.
Example: [[1,2],[3,4]] x [[2,0],[1,2]] gives [[4,4],[10,8]]. The top-left answer is 1x2 + 2x1 = 4.
Determinant and transpose
A determinant is one number from a square matrix. A 3x3 determinant needs more steps, so use the calculator output as a check while you study the expansion.
Transpose swaps rows and columns. Entry row 1, column 2 becomes row 2, column 1. This page keeps the grid at 2x2 and 3x3 so it stays readable on a phone.
Mistakes to check first
Addition and subtraction need the same matrix size. If the problem mixes sizes, the operation is not defined.
Do not flip multiplication order unless your teacher or source says to. Matrix A times Matrix B is a different question from Matrix B times Matrix A.
Worked examples for Matrix Calculator
[[4,4],[10,8]] because row 1 x column 1 is 1x2 + 2x1 = 4
[[6,8],[10,12]] by adding matching spots
7 because 3x5 - 4x2 = 15 - 8
-306
FAQ in plain language
What matrix operations are supported?
The Matrix Calculator supports addition, subtraction, multiplication, determinant, and transpose for 2x2 and 3x3 square matrices.
When can I add or subtract two matrices?
The two matrices need the same size. A 2x2 can add to another 2x2, and a 3x3 can add to another 3x3. Each answer spot comes from the matching spot in Matrix A and Matrix B.
What do the main Matrix Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Matrix Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Matrix Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
Does order matter for matrix multiplication?
Yes. Matrix multiplication is order-sensitive. A x B can be different from B x A because each answer entry uses a row from the first matrix and a column from the second.
What is a determinant?
A determinant is a single value calculated from a square matrix. For a 2x2 matrix [[a,b],[c,d]], the determinant is ad - bc.
Sources
Use these if you want to compare the formula, inputs, or limits with a trusted outside explanation.
Related tools
- Scientific Calculator A free scientific calculator for trig, logs, roots, powers, and constants.
- Quadratic Formula Calculator Solve ax^2 + bx + c = 0 with roots, discriminant, vertex, and steps.
- Big Number Calculator Add, subtract, multiply, and divide very large whole numbers exactly, including division remainders.
Keep exploring
If the matrix problem is only part of the assignment, these links keep you close to algebra and calculator pages that match it.
- Calculators Browse the full category for related tools that help with the same job.
- All free tools Search the complete Access Free Tools library by task, category, or tool name.
- All calculator and utility guides Find more plain-language examples, formulas, mistakes, and result explanations.
- Free calculator resources Start here when you are not sure which calculator page fits.
Privacy and copying results
Recent answers stay visible only while you work in the current browser tab. They are not sent to a server.
Use Copy answer when you want to save the inputs and result in notes, homework, a message, or a project list. Check the units, labels, and limits before copying.