Q. 25

If and (A + B)2 = (A2 + B2) then find the values of a and b.

Answer :

Given :


(A + B)2 = (A2 + B2)


To find : a and b


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


A + B = + = =


A + B =


(A + B)2 = × =


(A + B)2 = =


(A + B)2 =


A2 = × = =


A2 =


B2 = × = =


B2 =


(A2 + B2) = + =


(A2 + B2) =


It is given that (A + B)2 = (A2 + B2)


=


Equating similar terms in the given matrices we get,


2 – 2a = -a + 1 and -2b = -b + 1


2 – 1 = -a + 2a and -2b + b = 1


1 = a and -b = 1


a = 1 and b = -1


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