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 :

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 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 a prime number such that 3

Let p be prime number such that 3 < p < 50 , then p^2 - 1 is :

If p is a prime number,then LCM of p and (p+1) is