Two Values That Kill the Inverse — medium Determinants & Inverses problem | Incognition

Two Values That Kill the Inverse

Determinants & InversesMedium+20 XP+20

Two Values That Kill the Inverse

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?

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