(B) For a $2 \times 2$ matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$,the adjoint of $A$ is given by $\text{adj } A = \begin{bmatrix} d & -

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$\begin{bmatrix} 3 & 1 \\ -2 & 1 \end{bmatrix}$

(B) For a $2 \times 2$ matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$,the adjoint of $A$ is given by $\text{adj } A = \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$.Given $A = \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$,we have $a = 1, b = -1, c = 2, d = 3$.Substituting these values into the formula:$\text{adj } A = \begin{bmatrix} 3 & -(-1) \\ -2 & 1 \end{bmatrix} = \begin{bmatrix} 3 & 1 \\ -2 & 1 \end{bmatrix}$.Thus,the correct option is $B$.

Class 12 Mathematics 3-4. Matrices and Determinants Adjoint and inverse of matrices

Easy

If $A = \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$,then $\text{adj } A$ is equal to

A
$\begin{bmatrix} -3 & -1 \\ 2 & -1 \end{bmatrix}$
B
$\begin{bmatrix} 3 & 1 \\ -2 & 1 \end{bmatrix}$
C
$\begin{bmatrix} 3 & -2 \\ 1 & 1 \end{bmatrix}$
D
$\begin{bmatrix} 3 & -1 \\ -2 & 1 \end{bmatrix}$

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3-4. Matrices and Determinants

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Adjoint and inverse of matrices

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If $A = \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$,then $\text{adj } A$ is equal to

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