Evaluate the determinant: $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$

If $A = \begin{bmatrix} 5 & 5x & x \\ 0 & x & 5x \\ 0 & 0 & 5 \end{bmatrix}$ and $|A^2| = 25$, then $|x|$ is equal to

If matrix $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix}$,then the value of $a_{31} A_{31} + a_{32} A_{32} + a_{33} A_{33}$ is

Let $A = \begin{bmatrix} [x+1] & [x+2] & [x+3] \\ [x] & [x+3] & [x+3] \\ [x] & [x+2] & [x+4] \end{bmatrix}$,where $[t]$ denotes the greatest integer less than or equal to $t$. If $\operatorname{det}(A) = 192$,then the set of values of $x$ is the interval:

Let $A(a, 0)$,$B(b, 2b+1)$,and $C(0, b)$,where $b \neq 0$ and $|b| \neq 1$,be points such that the area of triangle $ABC$ is $1 \, \text{sq. unit}$. Then,the sum of all possible values of $a$ is:

If $\begin{bmatrix} 1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1 \end{bmatrix}$ is a singular matrix,then the value of $x$ is: