Let A be a non singular square matrix of $2 \times 2$. Then, $|adj\ A|$ is equal to

Let $A = [a_{ij}]_{3 \times 3}$ such that $|A| = -5$. Then the value of $\det(5A)$ is equal to

Which of the following are correct?

(A) $A=\begin{bmatrix}-9 & 4 & -3\\-1 & 0 & 4\\2 & 2 & 0\end{bmatrix}$ ; $a_{22}+a_{32}=-9$ where $a_{ij}$ denotes the $(i,j)^{th}$ element of matrix A.

(B) $A=\begin{bmatrix}2 & -2\\-2 & 2\end{bmatrix}$; $A^2=pA$, then $p=4$

(C) $\begin{bmatrix}8 & 6\\6 & 16\end{bmatrix}$ is a symmetric matrix

(D) $\begin{bmatrix}0 & -5 & 3\\5 & 0 & -7\\-3 & 7 & 0\end{bmatrix}$ is a symmetric matrix

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Which of the following statements are correct?

(A) Inverse of a matrix, if it exists, is unique

(B) $(kA)' = -kA'$ (where k is any real number)

(C) For an invertible matrix $A$, $(A^{-1})^{-1} = A$

(D) For an invertible matrix $A$, $(A')^{-1} = (A^{-1})'$

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If A and B are invertible matrices of the same order, then

Match List-I with List-II

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If $\begin{vmatrix} m! & (m+1)! & (m+2)! \\ (m+1)! & (m+2)! & (m+3)! \\ (m+2)! & (m+3)! & (m+4)! \end{vmatrix} = 2k$, where $m$ is a positive integer then which of the following are factors of $k$?

A. $m!$

B. $(m+1)!$

C. $(m+2)!$

D. $(m+3)!$

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If $A = \begin{bmatrix} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ then $|adj(3A^T)|^2$ is equal to