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Let A be a 2 xx 2 matrix with real entri...

Let A be a `2 xx 2` matrix with real entries. Let I be the `2 xx 2` identity matrix. Denote by tr (A), the sum fo diagonal entries of A. A ssume that `A^(2) = I`.
Statement 1 : If A != I and A ! = I, then det A = - 1.
Statement 2, If A != I and A ! = -I, then tr (A) != 0.

A

Statement 1 is false, statement 2 is true.

B

Statement 1 is true, statement 2 is true, statement 2 is correct explanation for statement 1.

C

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

D

Statement 1 is true, statement 2 is false.

Text Solution

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The correct Answer is:
D
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