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Let p be an odd prime number and Tp be t...

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.]

A

`(p-1)^(2)`

B

`2(p-1)`

C

`(p-1)^(2)+1`

D

`2p-1`

Text Solution

Verified by Experts

The correct Answer is:
D
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