Multiplying a Matrix by Another Matrix

1. Product Type: dot product

To multiply a matrix by another matrix we need to do the "dot product" of rows and columns:

2. Shape

To multiply an m×n matrix by an n×p matrix, the ns must be the same, and the result is an m×p matrix.

3. Identity Matrix

The "Identity Matrix" is the matrix equivalent of the number "1":

It is a special matrix, because when we multiply by it, the original is unchanged:

4. Order of Multiplication

Matrix multiplication is not commutative: