Multiplication of a Matrix by a Matrix:
For multiply two matrices, the first matrix must have the similar number of rows (m) as the second matrix has columns (n). Instead, m of the first matrix must equal n of the second matrix. For instance, a 2 x 1 matrix can be multiplied by a 1 x 2 matrix,
![2255_Multiplication of a Matrix by a Matrix.png](https://www.expertsmind.com/CMSImages/2255_Multiplication%20of%20a%20Matrix%20by%20a%20Matrix.png)
or a 2 x 2 matrix could be multiplied through a 2 x 2. If an m x n matrix is multiplied by an n x p matrix, after that the output matrix is an m x p matrix. For instance, if a 2 x 1 and a 1 x 2 are multiplied, the output will be a 2 x 2. If a 2 x 2 and a 2 x 2 are multiplied, the output will be a 2 x 2.
For multiply two matrices, the subsequent pattern is used:
![1034_Multiplication of a Matrix by a Matrix1.png](https://www.expertsmind.com/CMSImages/1034_Multiplication%20of%20a%20Matrix%20by%20a%20Matrix1.png)
In general terms, a matrix C which is a product of two matrices, A and B, will have elements given by the following.
cij = ai1b1j + aj2b2j + + + . . . + ainbnj
where
i = ith row
j = jth column