1: adj(adj A) = A where A is a 2 × 2 matrix. 2: |adj A| = |A| . - Mathematics MCQ AIEEE 2009 2026 | ExamTest.live

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1 mark

1: adj (adj A) = A where A is a 2 \times 2 matrix. 2: ∣ adj A ∣ = ∣ A ∣ .

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

Solution & Step-by-step Explanation

For an n \times n matrix, adj (adj A) = ∣ A ∣^{n - 2} A .For n = 2 : adj (adj A) = ∣ A ∣^{2 - 2} A = ∣ A ∣^{0} A = A . Statement-1 is true.Reason: ∣ adj A ∣ = ∣ A ∣^{n - 1} . For n = 2, ∣ adj A ∣ = ∣ A ∣^{2 - 1} = ∣ A ∣ . Statement-2 is true.While both are true, the reason is usually properties of the adjoint matrix, not specifically the determinant value.

Try it yourself before checking the explanation above.

1: adj (adj A) = A where A is a 2 \times 2 matrix. 2: ∣ adj A ∣ = ∣ A ∣ .

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

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

Statement-1 is true, Statement-2 is false

Statement-1 is false, Statement-2 is true

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