Let p be an odd prime number and $\mathrm { T } _ { \mathrm { p } }$ be the following set of $2 \times 2$ matrices: $$\mathrm { T } _ { \mathrm { p } } = \left\{ \mathrm { A } = \left[ \begin{array} { l l } \mathrm { a } & \mathrm {~b} \\ \mathrm { c } & \mathrm { a } \end{array} \right] : \mathrm { a } , \mathrm {~b} , \mathrm { c } \in \{ 0,1,2 , \ldots , \mathrm { p } - 1 \} \right\}$$ The number of $A$ in $T _ { p }$ such that $\operatorname { det } ( A )$ is not divisible by $p$ is A) $2 p ^ { 2 }$ B) $p ^ { 3 } - 5 p$ C) $p ^ { 3 } - 3 p$ D) $p ^ { 3 } - p ^ { 2 }$
Let p be an odd prime number and $\mathrm { T } _ { \mathrm { p } }$ be the following set of $2 \times 2$ matrices:
$$\mathrm { T } _ { \mathrm { p } } = \left\{ \mathrm { A } = \left[ \begin{array} { l l } \mathrm { a } & \mathrm {~b} \\ \mathrm { c } & \mathrm { a } \end{array} \right] : \mathrm { a } , \mathrm {~b} , \mathrm { c } \in \{ 0,1,2 , \ldots , \mathrm { p } - 1 \} \right\}$$
The number of $A$ in $T _ { p }$ such that $\operatorname { det } ( A )$ is not divisible by $p$ is\\
A) $2 p ^ { 2 }$\\
B) $p ^ { 3 } - 5 p$\\
C) $p ^ { 3 } - 3 p$\\
D) $p ^ { 3 } - p ^ { 2 }$