# An algebra problem

Algebra Level 4

Let $$D=\begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix}$$ and $$P=\begin{pmatrix} 7 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 0 & 5 \end{pmatrix}$$.

Consider $$A={ P }^{ -1 }DP$$. Find $$\det({ A }^{ 2 }+A)$$.

 Notation: $$\det(\cdot)$$ denotes the determinant function.

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