The set of values of K for which the system of equations $\begin{bmatrix} 2 & 3 & 1 \\ 4 & 5 & 0 \\ 1 & K & 3 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \\ 7 \end{bmatrix}$ gives a unique solution is :

If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew symmetric, then the value of $x+y$ is

If $\begin{vmatrix}1 & 1 & 1\\ c & b-x & a\\ b & a & c-x\end{vmatrix}=0$, then $x$ is equal to

If A is a square matrix of order 3 with $|A| = 4$, then the value of $|2\,adj\,A|$ is:

If A and B are symmetric matrices of order 3 x 3 then the matrix $2AB - BA$ is:

If $P\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} = \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix}$, then matrix P is equal to:

If A and B are two symmetric matrices of the same order, then