Question
Find a diagonal matrix $A$ that satisfies the given condition.$$A^{5}=\left[\begin{array}{rrr}1 & 0 & 0 \\0 & -1 & 0 \\0 & 0 & -1\end{array}\right]$$
Step 1
We know that when we raise a diagonal matrix to a power, it remains a diagonal matrix. Therefore, we can assume that matrix $A$ is also a diagonal matrix. Show more…
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