If \(A = \begin{bmatrix} 2 & -4 \\ 3 & 1 \end{bmatrix}\), then the adjoint of matrix \(A\) is _____.

Q.1 (ii) If \(A = \begin{bmatrix} 2 & -4 \\ 3 & 1 \end{bmatrix}\), then the adjoint of matrix \(A\) is _____.

A. \(\begin{bmatrix} 1 & 3 \\ 4 & -2 \end{bmatrix}\)

B. \(\begin{bmatrix} -1 & 3 \\ -4 & 1 \end{bmatrix}\)

C. \(\begin{bmatrix} -1 & -3 \\ -4 & 2 \end{bmatrix}\)

D. \(\begin{bmatrix} 1 & 4 \\ -3 & 2 \end{bmatrix}\)

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

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Answer: D. \(\begin{bmatrix} 1 & 4 \\ -3 & 2 \end{bmatrix}\)

Answer: (d) \(\begin{bmatrix} 1 & 4 \\ -3 & 2 \end{bmatrix}\)

Cofactors: \(A_{11} = 1,\ A_{12} = -3,\ A_{21} = -(-4) = 4,\ A_{22} = 2\). The adjoint is the transpose of the cofactor matrix: \(\operatorname{adj} A = \begin{bmatrix} 1 & 4 \\ -3 & 2 \end{bmatrix}\). (For a \(2\times 2\) matrix: swap the diagonal elements and change the signs of the other two.)

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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If \(A = \begin{bmatrix} 2 & -4 \\ 3 & 1 \end{bmatrix}\), then the adjoint of matrix \(A\) is _____.

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