Q. 2 A5.0( 5 Votes )

# Show that AB ≠ BA in each of the following cases : and

Given : and

Matrix A is of order 2 2 and Matrix B is of order 2 2

To show : matrix AB BA

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

For matrix AB, a = 2,b = c = 2,d = 2 ,thus matrix AB is of order 2 2

Matrix AB =

Matrix AB = =

Matrix AB =

For matrix BA, a = 2,b = c = 2,d = 2 ,thus matrix BA is of order 2 2

Matrix BA=

Matrix BA = =

Matrix BA =

Matrix BA = and Matrix AB =

Matrix AB BA

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