If $A = \begin{bmatrix} 3 & -2 \\ 4 & 2 \end{bmatrix}$,then $A^2 - 5A + 14I = 0$. Which of the following is equivalent to $A^2$?

Let $A = \begin{bmatrix} 5 & \sin^2 \theta & \cos^2 \theta \\ -\sin^2 \theta & -5 & 1 \\ \cos^2 \theta & 1 & 5 \end{bmatrix}$. Then the maximum value of $\det(A)$ is

If $P$ and $Q$ are two $3 \times 3$ matrices such that $|PQ|=1$ and $|P|=9$,then the determinant of $\text{adj}(P \cdot \text{adj}(3Q))$ is

If $A$ is a square matrix of order $3$ and $A^2+A+2I=0$,then

If $P$ and $Q$ are two non-singular matrices of the same order such that $Q^r = I$,for some integer $r > 1$,then $P^{-1}Q^{r-1}P - P^{-1}Q^{-1}P$ is equal to (where $I$ is the identity matrix and $O$ is the null matrix).

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: