I assume you're talking about two square matrices,
[tex]A=\begin{bmatrix}x^2&2\\x&1\end{bmatrix}[/tex]
and
[tex]B=\begin{bmatrix}x&2x\\3x&4x\end{bmatrix}[/tex]
If A is singular, then its determinant is 0:
[tex]\det A=x^2-2x=x(x-2)=0\implies x=0\text{ or }x=2[/tex]
B is not singular, so its determinant is not 0:
[tex]\det B=4x^2-6x^2=-2x^2\neq0[/tex]
This tells you x ≠ 0, so x = 2.
