# Four Ways to Multiply Matrices

## First: Row times Column

The entry in row I and column j of AB is (row i of A)*(column j of B)

## Second: Matrix A times every column of B

A[b1 … bp] = [Ab1 … Abp]
In this way, Each column of AB is a combination of the columns of A.

## Thrid: Every row of A times B

In this way, Each row of AB is a combination of the rows of B.

## Fourth: Column times Rows

Multiply columns 1 to n of A times rows 1 to n of B. Add those matrices.

Column times Row will produce a matrix, which has (size of the column of A)x(size of the row of B) size.
There is, (mn) times (np), We will get n matrices after we columns times rows, each matrix has (m * p) size.