Question

Multiplication of Matrices

Answer 1

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B.

In other words, for multiplication of two matrices A and B, the number of columns in A should be equal to the number of rows in B. Further more, for getting the elements of the product matrix, we take the rows of A and columns of B, multiply them element-wise and take the sum.

 AB = a₁b₁ + a₂b₂ + ......... + a_nb_n 

Using the product of a row matrix and a column matrix, let us now define the multiplication of any two matrices.

If A = (a_ij]_{m × n} and B =[b_ij]_{n × p} are two marices of orders m × n and n × p respectively, then their product AB is the matrix of order m x p and is defined as

(AB)_ij = (ith row of A) (jth column of B) for all i = 1,2, .... m and j = 1,2, ....... p

Note: If A and B are two matrices such that AB exists, then BA may or may not exist.