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

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

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

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

Solution

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