Find $adj$ $A$ for $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$.
- A$\begin{bmatrix} 4 & 3 \\ -1 & 2 \end{bmatrix}$
- B$\begin{bmatrix} -4 & -3 \\ -1 & 2 \end{bmatrix}$
- C$\begin{bmatrix} 4 & -3 \\ -1 & 2 \end{bmatrix}$
- D$\begin{bmatrix} 4 & -3 \\ 1 & 2 \end{bmatrix}$
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For any $2 \times 2$ matrix $A$,if $A(\text{adj } A) = \begin{bmatrix} 10 & 0 \\ 0 & 10 \end{bmatrix}$,then $|A| = $
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Suppose $n > 1$ and $A$ is a non-singular matrix of order $n$ such that $|\operatorname{adj} A| = |\operatorname{adj}(\operatorname{adj} A)|$. Then the matrix whose rank is $n$ is:
If $A$ is a square matrix of order $3$,then consider the following statements.
$I$. If $|A|=0$,then $|\operatorname{Adj} A|=0$
$II$. If $|A| \neq 0$,then $|A^{-1}|=|A|^{-1}$
Which of the above statements is/are true?
$I$. If $|A|=0$,then $|\operatorname{Adj} A|=0$
$II$. If $|A| \neq 0$,then $|A^{-1}|=|A|^{-1}$
Which of the above statements is/are true?
Let $P=[p_{ij}]$ and $Q=[q_{ij}]$ be two square matrices of order $3$ such that $q_{ij}=2^{(i+j-1)}p_{ij}$ and $\det(Q)=2^{10}$. Then the value of $\det(\text{adj}(\text{adj } P))$ is:
DifficultJEE MAIN 2026
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