JEE Math Practice Question

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 $${a^2} = I.$$ 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 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.