2x2 multiply
[[1,2],[3,4]] x [[2,0],[1,2]][[4,4],[10,8]] because row 1 x column 1 is 1x2 + 2x1 = 4
Matrix Calculator
Enter 2x2 or 3x3 matrices, then add, subtract, multiply, transpose, or find the determinant with plain steps and copyable answers.
2x2 and 3x3 Multiply matrices Determinants Transpose
Matrix A
Matrix B
Multiply 2x2[4, 4] [10, 8]
- Operation
- Multiply
- Size
- 2x2
- Uses Matrix B
- Yes
Steps
- Multiply each row of Matrix A by each column of Matrix B.
- Add each row-column product to fill the matching result entry.
- The result is [4, 4] [10, 8].
How to use the Matrix Calculator
- Choose 2x2 or 3x3 matrix size.
- Choose add, subtract, multiply, determinant, or transpose.
- Enter Matrix A and Matrix B when the operation needs both matrices.
- Press Calculate matrix to see the result, steps, examples, copy, and history.
What people use it for
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.
Quick examples
2x2 add
[[1,2],[3,4]] + [[5,6],[7,8]][[6,8],[10,12]] by adding matching spots
2x2 determinant
det([[3,4],[2,5]])7 because 3x5 - 4x2 = 15 - 8
3x3 determinant
det([[6,1,1],[4,-2,5],[2,8,7]])-306
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- How to use the Matrix Calculator See slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
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Frequently asked questions
Quick answers about matrix operations, multiplication order, determinants, supported sizes, and privacy.
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.
Why does the calculator only show 2x2 and 3x3 matrices?
Those sizes cover the quick checks most people need on this page, and they keep the grid readable on a phone. Bigger matrices need a different layout and slower step display.
Can this solve systems of equations?
Not yet. This version checks core matrix operations. If you are solving systems, use the result as one step in your work and still check the equation setup.
Can I use decimals or negative values?
Yes. Matrix entries can be positive, negative, whole, or decimal numbers.
Is my matrix history private?
Yes. Recent matrix answers stay only in the current browser tab while you use the page. They are not sent to a server.
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