Matrices & Determinants
General
Grade 12
Question:
<p>If $A = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$, then adj $A =$</p>
<p>$\begin{bmatrix} 1 & -2 \\ -2 & 1 \end{bmatrix}$</p>
<p>$\begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix}$</p>
<p>$\begin{bmatrix} 1 & -2 \\ -2 & -1 \end{bmatrix}$</p>
<p>$\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$</p>
Step-by-Step Solution
Key Concept: General
<div>$A = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$<br>Matrix formed by cofactors of $A = C = \begin{bmatrix} 1 & -2 \\ -2 & 1 \end{bmatrix}$<br>Transpose of Matrix $C = C^T = \begin{bmatrix} 1 & -2 \\ -2 & 1 \end{bmatrix}$<br>Adjoint of matrix $A = C^T = \text{adj } A = \begin{bmatrix} 1 & -2 \\ -2 & 1 \end{bmatrix}$</div>
Correct Answer: A