Let $A = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix}$,where $x, y$ and $z$ are real numbers such that $x + y + z > 0$ and $xyz = 2$. If $A^2 = I_3$,then the value of $x^3 + y^3 + z^3$ is ............

Let $A, B, C, D$ be square real matrices such that $C^T = DAB$,$D^T = ABC$,and $S = ABCD$. Then $S^2$ is equal to:

Let $1, \omega$ and $\omega^2$ be the cube roots of unity. If $S$ is the set of all non-singular matrices of the form $M = \begin{bmatrix} 1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1 \end{bmatrix}$ where $a, b, c \in \{\omega, \omega^2\}$,then the number of elements in $S$ is

Let $A = \begin{bmatrix} m & n \\ p & q \end{bmatrix}$,$d = |A| \neq 0$ and $|A - d(\operatorname{Adj} A)| = 0$. Then:

If $A(\theta)=\begin{bmatrix} i \sin \theta & \cos \theta \\ \cos \theta & i \sin \theta \end{bmatrix}$ is a matrix,where $i=\sqrt{-1}$,then which of the following is not true?

If $A$ and $B$ are two square matrices such that $B = -A^{-1}BA$,then $(A + B)^2 = $