Let $\mathbf{M} = \begin{pmatrix} 2 & 0 \\ 1 & -3 \end{pmatrix}.$  Find constants $a$ and $b$ so that
\[\mathbf{M}^{-1} = a \mathbf{M} + b \mathbf{I}.\]Enter the ordered pair $(a,b).$
Question:
Let $\mathbf{M} = \begin{pmatrix} 2 & 0 \\ 1 & -3 \end{pmatrix}.$  Find constants $a$ and $b$ so that
\[\mathbf{M}^{-1} = a \mathbf{M} + b \mathbf{I}.\]Enter the ordered pair $(a,b).$
Answer:
Let's think step by step.

user
\left( \frac{1}{6}, \frac{1}{6} \right)
Let $\mathbf{M} = \begin{pmatrix} 2 & 0 \\ 1 & -3 \end{pmatrix}.$  Find constants $a$ and $b$ so that
\[\mathbf{M}^{-1} = a \mathbf{M} + b \mathbf{I}.\]Enter the ordered pair $(a,b).$
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