Let $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2 \end{bmatrix}$. $M_{ij}$ and $A_{ij}$ respectively denote the minor and cofactor of an element $a_{ij}$ of matrix $A = [a_{ij}]$

(A) $M_{23} = 6$

(B) $A_{22} = -8$

(C) $A_{13} = 7$

(D) $M_{32} = -5$

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If $A$ and $B$ are invertible matrices of order 3. If $|A| = 2$ and $|(AB)^{-1}| = \dfrac{-1}{6}$, then the value of $|B|$ is :

Consider the system of equation $x+y+3z=8$, $2x+y+bz=24$, $x+ay+3z=10$, then which of the following statements are True?

(A) The system of equations has a unique solution if $a=2, b=3$

(B) The system of equations is inconsistent if $a=1, b \in R$ be any real number.

(C) The system of equations is inconsistent if $a \neq 1$, and $b \neq 6$

(D) The system of equations has a unique solution if $a=4$ and $b=3$.

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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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Let A and B be 3×3 matrices such that $A \neq B$. If $A^3 = B^3$ and $A^2B = B^2A$, then the determinant of $A^2 + B^2$ is:

If matrix $A=\begin{bmatrix}0&3a&-4\\2&1&2\\2b&2&-1\end{bmatrix}$ is a symmetric matrix, then the values of $a$ and $b$ are