Let S = M = a i j , a i j ∈ 0 , 1 , 2 , 1 ≤ i , j ≤ 2 be a sample space and A M ∈ S : M is invertible be an even. Then P A is equal to

Step-by-step solution

Given, S = M = a i j ,   a i j ∈ 0 , 1 , 2 ,   1 ≤ i , j ≤ 2 So, let M = a b c d where a , b , c , d ∈ 0 , 1 , 2 So, total sample space will be 3 4 = 81 Now we will find P A ¯ or possibilities for | M | = 0 So, for | M | = 0 cases will be, 1. 1 1 1 1 or 0 0 0 0 or 2 2 2 2 → Total matrix = 3 2. Two 1 ' s and Two 0 ' s → Total matrix = 4 3. Two 2 ' s and Two 0 ' s → Total matrix = 4 4. Two 1 ' s and Two 2 ' s → Total matrix = 4 5.