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Instructions

Let p be an odd prime number and $$T_p$$ be the following set of $$2 \times 2$$ matrices:

$$T_p = \left\{A = \begin{bmatrix}a & b \\c & a \end{bmatrix}:a, b, c \in \left\{0, 1, 2, ...., p-1\right\}\right\}$$

Question 43

The number of A in $$T_p$$, suchthat the trace of A is not divisible by p but det (A) is divisible by p is
[Note : The trace of a matrix is the sumofits diagonal entries.]

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The number of A in $$T_p$$, suchthat the trace of A is not divisible by p but det (A) is divisible by p is[Note : The trace of a matrix is the sumofits diagonal entries.]