Two Values That Kill the Inverse

20 pts · 20 coins

Determinants & InversesMedium

Consider the matrix

$A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & k & 6 \\ 3 & 6 & k \end{pmatrix}$

where $k$ is a real number. There are exactly two values of $k$ for which $A$ has no inverse.

What is the sum of those two values?

Select all that apply.