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

Question

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