How to Multiply Matrices | Linear Algebra, Matrix Operations, Matrix Multiplication

How do we multiply matrices? Matrix multiplication is one of the trickier matrix operations, but I hope this video lesson will help you understand it!

CORRECTION: At 6:21 I say "negative three times negative four", but we are actually doing negative three times positive four. I wrote it all correctly, just misspoke. Sorry about that!

When multiplying two matrices, the order matters (this means matrix multiplication is not commutative). If A and B are matrices, AxB is not necessarily equal to BxA, unlike with real numbers where order does not change the product. Furthermore, some matrices cannot even be multiplied together in a particular order!

The matrix on the left side of a multiplication has to have as many columns as the right matrix has rows. If this is not the case, then the matrices cannot be multiplied, so their product is undefined, it's like dividing by 0! If matrix A has dimensions 5x3 and matrix B has dimensions 3x4, then AxB is defined, because A as as many columns (3) as B has rows. However, BxA is not defined because B has 4 columns and A has 5 rows, and 4 is not equal to 5.

For more details on how to multiply two matrices, watch the video lesson!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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CORRECTION: At 6:21 I say "negative three times negative four", but we are actually doing negative three times positive four. I wrote it all correctly, just misspoke. Sorry about that!