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Let P be an odd prime number and T(p) be...

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

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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