Q. 25

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

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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