Find values of $x$ so that the matrix is invertible
$$A=\begin{pmatrix}
x & 0 & x \\
x & 2 & 1 \\
2x & 0 & 2x \\
\end{pmatrix}$$
I know that a matrix is invertible if determinant is not $0$, but I don't know how to find the $x$ values. I feel is a tricky question and this matrix will not be invertible no matter which value $x$ takes, but I don't know how to prove that either.
Best Answer
You just have to calculate it determinant:
$$ \det(A) = 4x^2 -4x^2 $$
Since it is always $0$ it is never invertibile.