The number of matrices A = a b c d , where a , b , c , d ∈ - 1 , 0 , 1 , 2 , 3 , … … , 10 , such that A = A - 1 , is ______.

Step-by-step solution

Given, A = a b c d and A = A - 1 So, A 2 = A · A - 1 = I ⇒ a b c d a b c d = 1 0 0 1 ⇒ a 2 + b c a b + b d a c + c d b c + d 2 = 1 0 0 1 On comparing both side we get, ∴     a 2 + b c = 1             ⋯ 1 a b + b d = 0           ⋯ 2 a c + c d = 0           ⋯ 3 b c + d 2 = 1             ⋯ 4 Now equation 1 - 4 gives a 2 - d 2 = 0 ⇒ a + d = 0 or a -