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Solve this following

Question:

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

Statement-1: $\operatorname{Tr}(\mathrm{A})=0$.

Statement-2: $|\mathrm{A}|=1$.

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

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

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

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

Correct Option: , 3

Solution:

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