Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

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

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (4) → $Adj A=\begin{bmatrix} 3 & -2\\ -1 & 1\\ \end{bmatrix}$

$A=\begin{bmatrix} 1 & 2\\ 1 & 3\\ \end{bmatrix}$

B = Co-factor matrix = $\begin{bmatrix} 3 & -1\\ -2 & 1\\ \end{bmatrix}$

$Adj A=B^T=\begin{bmatrix} 3 & -2\\ -1 & 1\\ \end{bmatrix}$