Let p be an odd prime number and `T_p`, be the following set of `2 xx 2` matrices `T_p={A=[(a,b),(c,a)]:a,b,c in {0,1,2,.........p-1}}` The number of A in `T_p`, such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is

Let p be an odd prime number and T_p be the following set of 2 x 2 matrices T_p={A=[(a,b),(c,a)]} , a,b,c in {0,1,2,…, p -1} The number of A in T_p such that A is either symmetric or skew-symmetric or both and det(A) is divisible by p is: [Note: the trace of a matrix is the sum of its diagonal entries.]

Let p be an odd prime number and T_p be the following set of 2 x 2 matrices T_p={A=[(a,b),(c,a)]} , a,b,c in {0,1,2,…, p -1} The number of A in T_p such that det(A) is not divisible by p, is :

Let P be an odd prime number and T_(p) be the following set of 2xx2 matrices : T_(P)={A=[(a,b),(c,a)]: a, b, c in {0, 1, ... , p-1}} The number of A in T_(P) such that det (A) is not divisible by p is

Let P be an odd prime number and T_(p) be the following set of 2xx2 matrices : T_(P)={A=[(a,b),(c,a)]: a, b, c in {0, 1, ... , p-1}} The number of A in T_(P) such that det (A) is not divisible by p is

Let P be an odd prime number and T_(p) be the following set of 2xx2 matrices : T_(P)={A=[(a,b),(c,a)]: a, b, c in {0, 1, ... , p-1}} The number of A in T_(P) such that det (A) is not divisible by p is

Let P be an odd prime number and T_(p) be the following set of 2xx2 matrices : T_(P)={A=[(a,b),(c,a)]: a, b, c in {0, 1, ... , p-1}} The number of A in T_(P) such that det (A) is not divisible by p is

Let p be an odd prime number and T_p be the following set of 2 x 2 matrices T_p={A=[(a,b),(c,a)]} , a,b,c in {0,1,2,…, p -1} The number of A in T_p such that the trace of A is not divisible by p but det(A) is divisible by p is :