If $A=\begin{bmatrix}2 & -1\\ -1 & 3\end{bmatrix}$, then the inverse of $(2A^{2}+5A)$ is
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Logic Tip: The Cayley-Hamilton theorem states that a matrix satisfies its own characteristic equation. $|A - \lambda I| = \lambda^2 - 5\lambda + 5 = 0 \implies A^2 - 5A + 5I = 0$. You can sometimes use this to reduce matrix polynomials ($A^2 = 5A - 5I$) before computing, trading matrix multiplication for simple addition.