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:

Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then $M$ is invertible if:

$A$ and $B$ are two $3 \times 3$ non-singular matrices such that $\operatorname{adj} A = |A| B$. If $\operatorname{tr}(X)$ denotes the trace of a square matrix $X$ and $C = \begin{bmatrix} 4 & 4 & 7 \\ 3 & -2 & 5 \\ -2 & 3 & 6 \end{bmatrix}$,then $\sum_{k=1}^{\infty} \operatorname{tr}\left(\frac{1}{3^k}(A B)^k C\right)$ is equal to

If $A = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} : a, b, c, d \in \{-1, 1\} \right\}$,then the number of singular matrices in $A$ is

Let $A=I_2-2 MM^{T}$,where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M=I_1$ holds. If $\lambda$ is a real number such that the relation $AX=\lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$,then the sum of squares of all possible values of $\lambda$ is equal to:

If $M$ and $N$ are square matrices of order $3$,then which one of the following statements is not true?