Matrix multiplication is intimately connected to linear transformations. In fact, matrix multiplication can be thought of as a way of representing and performing linear transformations.

Properties of matrix multiplication Learn Defined matrix operations Matrix multiplication dimensions

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The product of any square matrix and the appropriate identity matrix is always the original matrix, regardless of the order in which the multiplication was performed!

In this video, we learn how to evaluate expressions when a square matrix is given. We first evaluate a quadratic expression using a 2x2 matrix. We then evaluate a cubic expression using a 3x3 matrix.

You can only multiply matrices if the number of columns of the first matrix is the same as the number of rows as the second matrix. For example, say you want to multiply A x B.

It might be sometimes true, but in order for us to say that matrix multiplication is commutative, that it doesn't matter what order we are multiplying it, we have to figure out is this always going to be true?

Yes, matrix A multiplied with it's inverse A-1 (if it has one, and matrix A is a square matrix) will always result in the Identity matrix no matter the order (AA^-1 AND A^ (-1)A will give I, so they are the same).

Find the result of a multiplication of two given matrices.

And it's important to realize when we're doing matrix multiplication, that direction matters. I've actually given you some information here that-- we can't just assume when we were doing regular …