Let p be an odd prime number and $\mathrm{T}_{\mathrm{p}}$ be the following set of $2 \times 2$ matrices : $$ \mathrm{T}_{\mathrm{p}}=\left\{\mathrm{A}=\left[\begin{array}{ll} \mathrm{a} & \mathrm{~b} \\ \mathrm{c} & \mathrm{a} \end{array}\right]: \mathrm{a}, \mathrm{~b}, \mathrm{c} \in\{0,1, \ldots ., \mathrm{p}-1\}\right\} $$
The number of $A$ in $T_p$ such that the trace of $A$ is not divisible by $p$ but $\operatorname{det}(A)$ is divisible by $p$ is [Note: The trace of a matrix is the sum of its diagonal entries.]