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Let A be a {2}{2} matrix with real entries. Let I be the {2}{2

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Let A be a $2 \times 2$ matrix with real entries. Let I be the $2 \times 2$ identity matrix. Denote by 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 det $A = - 1$ .Statement 2: If $A \neq = I$ and $A \neq = - I$ , then $t r (A) \neq = 0$ .

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Let A be a

2 \times 2

matrix with real entries. Let I be the

2 \times 2

identity matrix. Denote by 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 det

A = - 1

.Statement 2: If

A \neq = I

and

A \neq = - I

, then

t r (A) \neq = 0

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Question Text	Let A be a $2 \times 2$ matrix with real entries. Let I be the $2 \times 2$ identity matrix. Denote by 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 det $A = - 1$ .Statement 2: If $A \neq = I$ and $A \neq = - I$ , then $t r (A) \neq = 0$ .
Answer Type	Video solution: 1
Upvotes	150