For a square matrix $A$ of order 3, if $\lvert A\rvert = -3$, then $\lvert 4\,adj A\rvert$ is equal to

Let $A = \begin{bmatrix} 0 & 2\alpha+1 \\ \ 1& \beta \end{bmatrix}$ and $B = \begin{bmatrix} b_{ij}\end{bmatrix}$ be a skew symmetric matrix of order 2 such that $b_{12} = 1$. If $AB = I_2$ where $I_2$ is identity matrix of order 2, then

If $A=\begin{bmatrix}4 & 1\\2 & 3\end{bmatrix}$ and $B=\begin{bmatrix}-2 & 3\\1 & 2\end{bmatrix}$ such that $2B-3A+X=0$ then $X$ is

If $A = \begin{bmatrix} 3 & 7 \\ 4 & -2 \end{bmatrix}$, $X = \begin{bmatrix} \alpha \\ -2 \end{bmatrix}$, $B = \begin{bmatrix} 7 \\ 32 \end{bmatrix}$ and $AX = B$, then the value of the $\alpha$ 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

Match List-I with List-II

Choose the correct answer from the options given below:

The value of $\begin{vmatrix} 2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x \end{vmatrix}$, where $x \neq 0$ is: