To do this, we need to solve the characteristic equation, which is given by:
$$\text{det}(A - \lambda I) = 0$$
For the given matrix A, this equation becomes:
$$\text{det}\begin{pmatrix} 5-\lambda & -4 \\ -3 & -3-\lambda \end{pmatrix} = (5-\lambda)(-3-\lambda) -
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