For what value(s) of k is A = \(\begin{bmatrix}3k^2 & 9 \\9 & k \end{bmatrix}\) is not a singular matrix

\(\mathbb R- \{-3\}\) \(\mathbb R- \{3\}\) \(\mathbb R- \{3,-3\}\) None of tjhese

\(\mathbb R- \{3\}\)

Firstly we start by determining the values where the matrix will be singular. Finding the determinant and equating it to 0. \(3 { k }^{ 3 } - 81 = 0\) \(3 ({ k }^{ 3 } - 27) = 0\) \({ k }^{ 3 } - 27= 0\) \({ k }^{ 3 } = 27\) k =3 So excluding these values, the matrix will be non-singular for all real values of k