Let A be a matrix of order 2 × 2 , whose entries are from the set 0 , 1 , 2 , 3 , 4 , 5 . If the sum of all the entries of A is a prime number p , 2 < p < 8 , then the number of such matrices A is

Step-by-step solution

Given, A = a b c d and a , b , c , d ∈ 0 , 1 , 2 , 3 , 4 , 5 Let, a + b + c + d = p , p ∈ 3 , 5 , 7 Case-i a + b + c + d = 3 where a , b , c , d ∈ 0 , 1 , 2 , 3 Entries will be 0 , 0 , 0 , 3   or   0 , 0 , 1 , 2   or   0 , 1 , 1 , 1 Number of ways = 4 ! 3 ! + 4 ! 2 ! + 4 ! 3 ! = 20         ⋯ 1 Case-ii a + b + c + d = 5 where a , b , c , d ∈ 0 , 1 , 2 , 3 , 4 , 5 Entries will be 0 , 0 , 0 , 5   or   0 , 0 , 1 , 4   or   0 , 0 ,