Let $A$ be a $2\times 2$ real matrix with entries from $\left\{0, 1\right\}$ and $\left|A\right|\ne 0$. Consider the following two statements;

$\left(P\right)$ If $A\ne l_2$, then $\left|A\right|=-1$

$\left(Q\right)$ If $\left|A\right|=1$, then $tr\left(A\right)=2$

Where $l_2$ denotes $2\times 2$ identity matrix and $tr\left(A\right)$ denotes the sum of the diagonal entries of $A$. Then