The value of x for which the matrix $\begin{bmatrix}-x & x & 2\\2 & x & -x\\x & -2& -x\end{bmatrix}$ will be non-singular, are

∀ x other than 2 and -2

The correct answer is option (2) : ∀ x other than 2 and -2

The given matrix will be non-singular ,if

$⇒\begin{bmatrix}-x & x & 2\\2 & x & -x\\x & -2& -x\end{bmatrix}≠0$

$⇒-x(-x^2-2x)-x(-2x+x^2)+2(-4-x^2)≠0$

$⇒2x^2-8≠0⇒x≠\pm 2$