If $A$ is a $3\times 3$ matrix with $|A|=4$, then $|4A|$ is equal to :

$A = \begin{bmatrix} 1/3 & 2 \\ 0 & 2x - 3 \end{bmatrix}$ & $B = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$ If $AB = I$ (Where I is an identity matrix of order 2) , then value of x is

Match List-I with List-II

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If A is a square matrix of order 3 and $|A|$ is 2, then value of $|adj(A)|$ is :

If $A=[a_{ij}]_{3\times3}=\begin{bmatrix}2 & 3 & -1\\1 & 2 & 3\\0 & -1 & 1\end{bmatrix}$ and $B=[b_{ij}]_{3\times2}=\begin{bmatrix}3 & -2\\1 & 4\\1 & 2\end{bmatrix}$ then the value of $a_{12}b_{21}+a_{32}b_{31}$ is

The system of equations in 3 variables $x, y$ and $z$ as $x+y=5$, $y+az=3$, $x+by=8$ has a unique solution if the value of $a$ and $b$ are

(A) $a=1, b=1$

(B) $a=0, b=1$

(C) $a \in (-\infty,0)$ and $b\neq1$

(D) $a\neq0$ and $b\in(3,4)$

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If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then the value of $A^{20}$ is: