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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