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Two matrices can be multiplied
together only when
the number of columns in the matrix on the left equals the number of rows in
the matrix on the right.

For example, suppose

The matrix product AB is only defined in M = L.

The resulting matrix will be of size N x R.

It is performed by multiplying each row of A by each column of B

There are terms for describing the order of matrix multiplication

For example, in the matrix product**AB**,

**Example:**

For example, suppose

- matrix A is N x M
- matrix B is L x R

The matrix product AB is only defined in M = L.

The resulting matrix will be of size N x R.

It is performed by multiplying each row of A by each column of B

There are terms for describing the order of matrix multiplication

- When
a matrix appears on the left, it is
*pre-multiplied*. - When
a matrix appears on the right, it is
*post-multiplied*.

For example, in the matrix product

**A**is pre-multiplied to**B****B**is post-multiplied to**A**

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