Math & Algebra Tool
Matrix Multiplication
Multiply two matrices step-by-step.
Dimensions
Matrix A:x
Matrix B:x
Matrix A
Matrix B
Frequently Asked Questions
How do you multiply two matrices?+
To find the entry in row 'i' and column 'j' of the result, you multiply each element in row 'i' of the first matrix by the corresponding element in column 'j' of the second matrix, and sum them up (Dot Product).
When is matrix multiplication impossible?+
Multiplication is only possible if the number of columns in the first matrix (Matrix A) exactly equals the number of rows in the second matrix (Matrix B). Our calculator handles this check for you.
Is Matrix Multiplication commutative?+
Generally, No. A x B is usually not the same as B x A. This is a key difference between matrix algebra and regular number multiplication.
What is an Identity Matrix?+
The Identity Matrix (I) acts like the number 1. Any matrix multiplied by the Identity Matrix stays the same (A x I = A). It has 1s on the diagonal and 0s elsewhere.
Why do we use matrices?+
Matrices are efficiently used to solve systems of linear equations, transform geometric objects (rotate/scale) in computer graphics, and model complex systems in physics and economics.
Does the size of the result matrix change?+
Yes. If you multiply an (m x n) matrix by an (n x p) matrix, the result will be an (m x p) matrix. Essentially, the inner dimensions cancel out.