If and , show that AB is a zero matrix.

Given : and

Matrix A is of order 3 3 , matrix B is of order 3 3 and matrix C is of order 3 3

To show : AB is a zero matrix

Formula used :

Where c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

If A is a matrix of order a b and B is a matrix of order c d ,then matrix AB exists and is of order a d ,if and only if b = c

If A is a matrix of order a b and B is a matrix of order c d ,then matrix BA exists and is of order c b ,if and only if d = a

= 0 matrix

Hence, Proved