# Matrix to Polynomial

Algebra Level 5

Let $$\rho: GL(2,\mathbb{R}) \rightarrow \mathbb{R}_{[x]}$$, $$\forall A\in GL(2,\mathbb{R})$$ we defined $$\rho(A) = det(xI_{2} - A)$$. Find $$det(A)$$ if $$det(xI_{2} - A) = x^2 -900x + 100$$.

Details : $$AI_{2} = A = I_{2}A$$

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