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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 A is either symmetric or skew-symmetric or both, and det (A) divisible by p, is

A

`2p^(2)`

B

`p^(3)-5p`

C

`p^(3)-3p`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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RESONANCE ENGLISH-MATRICES & DETERMINANT-EXERCISE-3
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