Engineering Mathematics Linear Algebra Eigenvalues

Let \(\rm \begin{pmatrix}2&a\\\ b&c\end{pmatrix}\) be a 2 x 2 real matrix for which 6 is an eigenvalue. Which of the following statements is necessarily true?

1
24 - ab = 4c
2
a + b = 8
3
c = 6
4
ab = 0

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