Let A be a 2 × 2 matrix with non-zero entries and let A^2 = I .Statement-1: Tr(A) = 0 Statement-2: |A| = 1 - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Let A be a 2 \times 2 matrix with non-zero entries and let A^{2} = I .Statement-1: Tr (A) = 0 Statement-2: ∣ A ∣ = 1

A $Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1.$
B $Statement-1 is true, Statement-2 is false.$
C $Statement-1 is false, Statement-2 is true.$
D $Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1.$

Solution & Step-by-step Explanation

Let A = (a c b d) . A^{2} = I ⟹ ∣ A ∣^{2} = 1 ⟹ ∣ A ∣ = \pm 1 . A^{2} = (a^{2} + b c c (a + d) b (a + d) d^{2} + b c) = (1001) .If b, c \neq = 0, then a + d = 0, so Tr (A) = a + d = 0 . (Statement 1 is True).Then b c + a^{2} = 1 and ∣ A ∣ = a d - b c = a (- a) - b c = - (a^{2} + b c) = - 1 .So ∣ A ∣ = - 1 . Statement 2 says ∣ A ∣ = 1, which is False.

Try it yourself before checking the explanation above.

Let A be a 2 \times 2 matrix with non-zero entries and let A^{2} = I .Statement-1: Tr (A) = 0 Statement-2: ∣ A ∣ = 1

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1.

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

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

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

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