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 c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

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