# Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr(A), the sum of diagonal entries of a. Assume that A2 = I. Statement-1 : If A ¹ I and A ¹ –I, then det (A) = –1 Statement-2 : If A ¹ I and A ¹ –I, then tr (A) ¹ 0.

Question:

Let $A$ be $a 2 \times 2$ matrix with real entries. Let $I$ be the $2 \times 2$ identity matrix. Denote by $\operatorname{tr}(A)$, the sum of diagonal entries of $a$. Assume that $A^{2}=I$.

Statement-1: If $A \neq I$ and $A \neq-I$, then $\operatorname{det}(A)=-1$

Statement-2 : If $A \neq I$ and $A \neq-I$, then $\operatorname{tr}(A) \neq 0$.

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

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

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

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

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Matrices and Determinants chapter.
JEE Main Previous Year 2008

Solution:

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