The matrix A^2+4A-5I, where I is the identity matrix and A=pmatrix1&24&-3pmatrix, equals:

Question

The matrix $A^2+4A-5I$, where $I$ is the identity matrix and $A=\begin{pmatrix}1&2\4&-3\end{pmatrix}$, equals:

Accepted Answer

$A^2=\begin{pmatrix}9&-4\-8&17\end{pmatrix}$.

$$A^2+4A-5I=\begin{pmatrix}9&-4\-8&17\end{pmatrix}+\begin{pmatrix}4&8\16&-12\end{pmatrix}-\begin{pmatrix}5&0\0&5\end{pmatrix}=\begin{pmatrix}8&4\8&0\end{pmatrix}=4\begin{pmatrix}2&1\2&0\end{pmatrix}.$$

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