Find the matrix $\mathbf{M},$ with real entries, such that
\[\mathbf{M}^3 = \begin{pmatrix} 19 & 30 \\ -45 & -71 \end{pmatrix}.\]
Question:
Find the matrix $\mathbf{M},$ with real entries, such that
\[\mathbf{M}^3 = \begin{pmatrix} 19 & 30 \\ -45 & -71 \end{pmatrix}.\]
Answer:
Let's think step by step.

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\begin{pmatrix} 1 & 2 \\ -3 & -5 \end{pmatrix}
Find the matrix $\mathbf{M},$ with real entries, such that
\[\mathbf{M}^3 = \begin{pmatrix} 19 & 30 \\ -45 & -71 \end{pmatrix}.\]
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