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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 the trace of A is not divisible by p but det(A) is divisible by p is :

A

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

B

`p^(3)-(p-1)^(2)`

C

`(p-1)^(2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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