I am stuck on the following problem:
Let $L$ denotes the set of all primes $p$ such that the following matrix is invertible when considered as a matrix with entries in $\Bbb Z/p \Bbb Z$ .
$A=\begin{pmatrix} 1 &2 &0 \\ 0 &3 &-1 \\ -2 &0 &2 \end{pmatrix}$
Then how can I verify whether the following statements are true/false?
- $L$ contains all the prime numbers greater than $10$
- $L$ contains all the prime numbers other than $2$ and $5$
- $L$ contains all the prime numbers
- $L$ contains all the odd prime numbers.
Can someone give explanation?Thanks Thanks in advance for your time.