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Let p be an odd prime number and $$T_p$$ be the following set of $$2 \times 2$$ matrices:
$$T_p = \left\{A = \begin{bmatrix}a & b \\c & a \end{bmatrix}:a, b, c \in \left\{0, 1, 2, ...., p-1\right\}\right\}$$
The number of A in $$T_p$$, such that det (A) is not divisible byp is
$$2p^2$$
$$p^3 - 5p$$
$$p^3 - 3p$$
$$p^3 - p^2$$
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