Jee Advanced
Matrices And Determinants
IIT-JEE 2010 Paper 1 Offline
MCQ+3 / -12010
Let $p$ be an odd prime number and $T_p$ be the following set of $2 \times 2$ matrices :
$$ \mathrm{T}_{\mathrm{p}}=\left\{\mathrm{A}=\left[\begin{array}{ll} a & b \\ c & a \end{array}\right]: a, b, c \in\{0,1,2, \ldots, p-1\}\right\} $$
The number of $A$ in $T_p$ such that $A$ is either symmetric or skew-symmetric or both, and $\operatorname{det}(\mathrm{A}) \operatorname{divisible}$ by $p$ is :