The set of real values of a for which the matrix

Given: The matrix $A=\left[\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right]$ is non-singular

$A$ is non-singular $\Rightarrow|A| \neq 0$

Thus,

$\left|\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right| \neq 0$

$\Rightarrow 4 a-4 \neq 0$

$\Rightarrow 4 a \neq 4$

$\Rightarrow a \neq 1$

$\Rightarrow a \in R-\{1\}$

Hence, the set of real values of a for which the matrix $A=\left[\begin{array}{ll}a & 2 \\ 2 & 4\end{array}\right]$ is non-singular is $R-\{1\}$