Q. 54.6( 5 Votes )

If and , show that AB is a zero matrix.

Answer :

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


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