Let p be an odd prime number and Tp be the following set of 2 × 2 matrices.
Tp = { A :
= a, b where a, b,c belongs to {0, 1, 2, ..., p -1}
c ,a
please note that here a,b,c are the elements of matrices ( a,b are in first row and c,a are in second row)
Q 1. The number of A in Tp such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is-------
Q2.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---
Q3The number of A in Tp such that det (A) is not divisible by p is----