Question
Let A be a 2 × 2 matrix with non-zero entries and let A2 = I, where I is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.
Statement-1: Tr(A) = 0.
Statement-2: |A| = 1.
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Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
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Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.
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Statement-1 is true, Statement-2 is false.
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Statement-1 is false, Statement-2 is true.
Solution
C.
Statement-1 is true, Statement-2 is false.
A satisfies A2 -Tr(A). A + (det A) l = 0
on comparing with A2-I = 0,
we get
Tr (A) = 0, |A| = - 1
