If $A = \begin{bmatrix} -8 & 5 \\ 2 & 4 \end{bmatrix}$ satisfies the equation $x^2 + 4x - p = 0$, then $p$ is equal to

Give the correct order of initials $T$ or $F$ for following statements. Use $T$ if statement is true and $F$ if it is false.
Statement $-1$ : If $A$ is an invertible $3 \times 3$ matrix and $B$ is a $3 \times 4$ matrix,then $A^{-1}B$ is defined.
Statement $-2$ : It is never true that $A + B, A - B$,and $AB$ are all defined.
Statement $-3$ : Every matrix none of whose entries are zero is invertible.
Statement $-4$ : Every invertible matrix is square and has no two rows the same.

Let $a, b, c \in \mathbb{R}$ be all non-zero and satisfy $a^{3}+b^{3}+c^{3}=2$. If the matrix $A=\begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix}$ satisfies $A^{T} A=I$,then a value of $abc$ can be

Let $A$ and $B$ be two $3 \times 3$ matrices such that $AB = I$ and $|A| = \frac{1}{8}$. Then $|\operatorname{adj}(B \operatorname{adj}(2A))|$ is equal to:

If $x, y$ are any two non-zero real numbers, $a_{i j} = xi + yj$, $A = \{a_{i j}\}_{n \times n}$ and $P, Q$ are two $n \times n$ matrices such that $A = xP + yQ$, then

If $A$ is a non-singular matrix of order $3$ such that $(A-2I)(A-4I)=0$,then $\frac{1}{6}A + \frac{4}{3}A^{-1}$ is (where $I$ is a unit matrix of order $3$ and $0$ is a null matrix of order $3$).