If $A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}$ and $A = A^{-1}$,then $x = \dots$

If $A$ and $B$ are square matrices of the same order and $AB = 3I$, then $A^{-1}$ is equal to

Let $A$ be a $3 \times 3$ matrix such that $A^T + 2A = I$. Then $\det(A^{-1})$ is equal to:

Which of the following is true for the matrix product $AB$?

If $A$ is a square matrix of order $3$ such that $\operatorname{det}(A)=3$ and $\operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2A)^{-1}\right)\right)\right)\right)\right)=2^{m} 3^{n}$,then $m+2n$ is equal to:

If $A = [a_{ij}]_{3 \times 3}$ is a matrix such that $a_{ij} = |2i - 5j|$, where $|.|$ denotes the modulus function, then the element in the $2^{nd}$ row and $3^{rd}$ column of $A^{-1}$ is ...