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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 det(A) is not divisible by p, is :

A

`2p^(2)`

B

`p^(3)-5p`

C

`p^(3)-3p`

D

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

Text Solution

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The correct Answer is:
D
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