Let p be an odd prime number and T be the following set of 2X2 matrices,

T={A=matrix such that a11=a, a12=b, a21=c, a22=a where aij denotes the term in ith row and jth column

a,b,c belongs to {0,1,2,........,p-1}

THen number of A in T such that trace of A is not divisible by p but det(A) is divisible by p is?

trace of matrix isthe sum of its diagnol entries.