š² Matrix Calculator
Matrices are grids of numbers that add entry-by-entry, but multiply in a row-times-column dance: each entry of the answer is a whole dot product. Type your two 2Ć2 grids, pick the operation, and the result appears instantly.
Matrix multiplication is not commutative ā AĆB and BĆA usually differ ā so the order you enter the matrices is the order they are multiplied.
How to use this calculator
Fill in the eight entries of matrices A and B, pick add or multiply, and press Calculate for the result matrix.
- Type the four entries of matrix A, row by row.
- Type the four entries of matrix B, row by row.
- Choose Add (A + B) or Multiply (A x B).
- Press Calculate and read the result in bracket form.
Frequently asked questions
What does this matrix calculator compute?
It adds or multiplies two 2x2 matrices. Addition works entry by entry; multiplication uses the row-times-column rule where each answer entry is a dot product of a row of A with a column of B.
Can you show a worked example?
With A = [[1,2],[3,4]] and B = [[5,6],[7,8]], the sum is [[6,8],[10,12]] and the product is [[19,22],[43,50]]. Try swapping A and B in multiply mode to see the different answer.
Does the order matter in multiplication?
Yes. Matrix multiplication is not commutative, so A times B and B times A usually give different results. The calculator always multiplies in the order you entered them.
Why only 2x2 matrices?
Two-by-two keeps the input quick while covering homework, graphics transforms and the core ideas. The same rules scale up to bigger matrices in textbooks and software.