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