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Let A be a 2 xx 2 matrix with non-zero e...

Let A be a `2 xx 2` matrix with non-zero entries and let A^2=I, where i is a `2 xx 2` identity matrix, Tr(A) i= sum of diagonal elements of A and `|A|` = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2:`|A|`=1

A

Statement-1is true, Statement-2 is true and Statement-2 is not correct explantion for Statement-1.

B

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

C

Statement-1 is false, Statement-2 is true

D

Statement-1 is true, Statement-2 is true and Statement-2 is a correct explantion for Statement-1.

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The correct Answer is:
B
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Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume 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 t r(A)!=0 .

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