The number of A in Tp such that the trace of A is not divisible by p but det(A) is divisible by p is?

acannot be equal to 0 as the trace would be divisible byp.Hence,acan acquire values from1,2,...,p𕒵Now let us select some value ofafrom the given set of values.Let the remainder ofa2berwhen divided byp.Now,a2−bcmust be divisible byp. Hence,bcmust have the remainderrwhen divided byp.Now,borccannot be 0.If we select some value ofbfrom1,2,...,n𕒵, we can exactly have one value ofcsuch that the remainder ofbcis r.We can selectbinp𕒵ways.For every value ofa,bcan be selected inp𕒵ways.acan be selected inp𕒵ways.Hence, total number of possible matrices=(p𕒵)×(p𕒵)