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 cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj
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
1