If $A=\left[\begin{array}{cc}i & 0 \\ 0 & -i\end{array}\right]$,$B=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]$ and $C=\left[\begin{array}{cc}0 & i \\ i & 0\end{array}\right]$,then which of the following is true?

Let $\left| \begin{array}{ccc} (a-x)^2 & (a-y)^2 & (a-z)^2 \\ (b-x)^2 & (b-y)^2 & (b-z)^2 \\ (c-x)^2 & (c-y)^2 & (c-z)^2 \end{array} \right| = \frac{-351}{8}$. If $x, y, z$ are the roots of the equation $8t^3 - 62t^2 + 43t - 7 = 0$ and $a, b, c$ are distinct numbers,then the value of $|(a-b)(b-c)(c-a)|$ is:

If $A$ and $B$ are square matrices of the same order such that $AB = A$ and $BA = B$,then $(A + I)^5$ is equal to (where $I$ is the identity matrix).

If $A = \int\limits_1^{\sin \theta } {\frac{t}{{1 + {t^2}}}} dt$ and $B = \int\limits_1^{\csc \theta } {\frac{dt}{{t\left( {1 + {t^2}} \right)}}} $,(where $\theta \in \left( {0, \frac{\pi }{2}} \right)$),then the value of $\left| {\begin{array}{*{20}{c}} A & {{A^2}} & { - B} \\ {{e^{A + B}}} & {{B^2}} & { - 1} \\ 1 & {{A^2} + {B^2}} & { - 1} \end{array}} \right|$ is

If $A=\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$,prove that $A^{n}=\begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}$ for all $n \in N$.

If $D_1$ and $D_2$ are two $3 \times 3$ diagonal matrices,then