If $X$ is a square matrix of order $3 \times 3$ and $\lambda$ is a scalar,then $adj(\lambda X)$ is equal to

If $B = \begin{bmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{bmatrix}$ is the inverse of a $3 \times 3$ matrix $A$,then the sum of all values of $\alpha$ for which $\det(A) + 1 = 0$ is:

If $A$ and $B$ are non-singular square matrices of the same order,then $adj(AB)$ is equal to:

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

If matrices $X$ and $Y$ are inverses of each other,then which of the following is true?

If $A = \begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix}$ and $\text{adj } A = \begin{bmatrix} 5 & x & -2 \\ 1 & 1 & 0 \\ -2 & -2 & y \end{bmatrix}$,then the value of $x+y$ is: