If $A = \begin{bmatrix} 3 & 2a \\ 1 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 2 & 3 \\ b & 5 \end{bmatrix}$ both are singular matrices, then $a + b$ is equal to

If A is an invertible matrix of order 2, then $\det(( {adj } A)^{-1})$ is equal to

If $\begin{bmatrix} 1 & 0 \\ b & 5 \end{bmatrix} + 2\begin{bmatrix} a & 0 \\ 1 & -2 \end{bmatrix} = I$, where $I$ is a unit matrix of order 2, then the value of $(a - b)$ is:

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$ is a matrix such that $A^2 = 8A + KI$,where $I$ is an identity matrix of order 2 then value of $K$ is :

If $A^2 = 8A + kI, A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ then value of $k$ is:

If $a,b,c$ are the roots of $x^3+px+q=0$, then the value of $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ is equal to

For what value of k, the following system of equations has infinitely many solutions?

$x + 2y = 5, 3x + ky = 15$