Let $A$ be a $2\times 2$ matrix with real entries. Let $I$ be the $2\times 2$ identity matrix. Denote by $\text{tr}(A)$ the sum of diagonal entries of $A$. Assume $A^2=I$.Statement - 1: If $A\ne I$ and $A\ne -I$, then $\det A=-1$.Statement - 2: If $A\ne I$ and $A\ne -I$, then $\text{tr}(A)\ne 0$.

1. A
   Statement - 1 is false, Statement - 2 is true
2. B
   Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1
3. C
   Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1
4. D
   Statement - 1 is true, Statement - 2 is false