JEE Math Practice Question

Let $$A$$ be a $$\,2 \times 2$$ matrix with non-zero entries and let $${A^2} = I,$$ where $$I$$ is $$2 \times 2$$ identity matrix. Define $$Tr$$$$(A)=$$ sum of diagonal elements of $$A$$ and $$\left| A \right| = $$ determinant of matrix $$A$$. Statement- 1: $$Tr$$$$(A)=0$$. Statement- 2: $$\left| A \right| = 1$$ .

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