If $\begin{vmatrix} 2+x & y & z \\ x & 2+y & z \\ x & y & 2+z \end{vmatrix} = 0$, then the value of $x+y+z$ is

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

If $A=\begin{bmatrix}1&1&1\\1&0&2\\3&1&1\end{bmatrix}$ and $B=\begin{bmatrix}-2&0&2\\5&-2&-1\\1&2&-1\end{bmatrix}$ such that AB=4I (where I is identity matrix) then solution of system of equations $x+y+z=6, x+2z=7, 3x+y+z=12$ is

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

If $\begin{vmatrix} 1 & \cos \theta & 0 \\ \sin \theta & 1 & \cos \theta \\ |\cos \theta & 1 & -\sin \theta| \end{vmatrix} = A\sin \theta + B\cos \theta + C\sin \theta\cos \theta$ then:

The number of all possible matrices of order $2 \times 3$ with entries -1 or 1 is

The difference of two different skew-symmetric matrices is: