The system of equation $2x + \lambda y = 8$, $\lambda x + 8y = 3$ has a unique solution if the value of $\lambda$ is (are):

If A is a matrix of order $m \times n$ and B is another matrix such that $A'B$ and $BA'$ are both defined, then the order of matrix B is

If A and B are square matrices of order 3 such that $|A| = 3$ and $|B| = -1$, then $|3AB|$ is equal to

If $a, b$ and $c$ are non-zero real number such that $\begin{vmatrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{vmatrix} = 0$, then value of $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}$ is

If $\begin{vmatrix} 3x & 4 \\ 7 & x \end{vmatrix} = \begin{vmatrix} 6 & 3 \\ 2 & 1 \end{vmatrix}$ then :

Let $A = \begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}$, $B = \begin{bmatrix} 4 & 6 \\ -2 & 2 \end{bmatrix}$ and $C$ be a matrix such that $C = AB$. Then $|(BC)^{-1}|$ is equal to

The matrix $X$ in the equation $AX = B$, such that $A = \begin{bmatrix} 1 & 3 \\ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix}$ is given by