Let $A$ be a $2×2$ real matrix with entries from $\{0, 1\}$ and $|A|\neq0$. Consider the following two statements :

(P)$\quad \text{If }A \neq I_2, \text{then }|A|=-1$

(Q)$\quad \text{If }|A|=1, \text{then }tr(A)=2$

where $I_2$ denotes $2×2$ identity matrix and $tr(A)$ denotes the sum of the diagonal entries of $A$. Then :

(1) (P) is true and (Q) are false

(2) Both (P) and (Q) are true

(3) Both (P) and (Q) are false

(4) (P) is false and (Q) is true

(P)$\quad \text{If }A \neq I_2, \text{then }|A|=-1$

(Q)$\quad \text{If }|A|=1, \text{then }tr(A)=2$

where $I_2$ denotes $2×2$ identity matrix and $tr(A)$ denotes the sum of the diagonal entries of $A$. Then :

(1) (P) is true and (Q) are false

(2) Both (P) and (Q) are true

(3) Both (P) and (Q) are false

(4) (P) is false and (Q) is true