Just like, addition and subtraction of two matrices, we can multiply two or more than two matrices. Matrix multiplication is a binary operation. We can multiply two or more than two matrices and produce another matrix.

Here, we will learn the following in detail:

• Multiplying 2x2 Matrices
• Multiplying 3x3 Matrices
• Matrix Multiplication Rules
• Matrix Multiplication Properties

## Matrix Multiplication Rules

If A and B are the two matrices then, we can multiply A by B if and only if, the number of columns in the first matrix is equal to the number of rows in the second matrix.

The product of matrices is undefined, if the rules for multiplying matrices defined above is not satisfied. After multiplication, the order of the resultant matrix is (number of rows of first matrix) × (number of columns of second matrix).So, if Apxq and Bqxr are two matrices then, the product of these two, say C is a matrix of order pxr. AB = {aij] x [bjk] = [ cik ]pxr, where cik =$\sum_{j=1}^{q} a_{ij}.b_{jk}$