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 A is a square matrix of order $n$ and $k$ is a scalar such that $|kA| = \alpha|A|$ then the value of $\alpha$ is:

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

If $\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}\mathrm{n} \\ 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}8 \\ 11\end{array}\right]$ and $A X=B$, then the value of $n$ will be :

Let $A=\begin{bmatrix}2 & 2 & 2 \\ 0 & 2 & 2 \\ 0 & 0 & 2\end{bmatrix}$, then $A^6$ is equal to:

If matrix $A = \begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$ and $A' = A$, then :

If $A = \begin{bmatrix} 1 & 5 \\ 7 & 12 \end{bmatrix}, B = \begin{bmatrix} 9 & 1 \\ 7 & 8 \end{bmatrix}$ and C are three matrices such that $3A + 5B + 2C = 0$, then the matrix C is equal to