Matrices and Determinants

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: $$\left| A \right| = 1$$ .