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 $\text{Tr}\left(A\right)=$ sum of diagonal elements of A and $\left|A\right|=$ determinant of matrix A.

Statement-1: $\text{Tr}\left(A\right)=0$

Statement-2: $\left|A\right|=1$

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Statement-1 is true, Statement-2 is false

Statement-1 is false, Statement-2 is true.