For what value(s) of k is A = \(\begin{bmatrix}3k & 2 \\6 & k \end{bmatrix}\) is not a singular matrix

\(\mathbb R- \{-2,2\}\)

Firstly we start by determining the values where the matrix will be singular.

Finding the determinant and equating it to 0.

\(3 { k }^{ 2 } - 12 = 0\) \(3 ({ k }^{ 2 } - 4) = 0\)

\({ k }^{ 2 } - 4= 0\) \({ k }^{ 2 } = 4\)

k =2 or -2

So excluding these values, the matrix will be non-singular for all real values of k