Question

The number of $A$ in $T_P$, such that det $\left(A\right)$ is not divisible by $p$ is

• A. $2p^2$
• B. $p^3-5p$
• C. $p^3-3p$
• D. $p^3-p^2$.

Answer 1

Answer: (D)

$p^3-p^2$.

Total number of $A=p\times p\times p=p^3$

Number of A such that $det\left(A\right)$divisible by p

$={(p-1)}^2+$no. of A in which $a=0$

$={(p-1)}^2+p+p-1=p^2$

Required number$=p^3-p^2$

Option D