Discussion
The inverse of the matrix with rows (2, 1) and (1, 1) is the matrix with rows
Answer: D
The determinant is \( (2)(1)-(1)(1)=1 \), so the inverse is the adjoint itself:
\[ A^{-1} = \frac{1}{\det A}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix} = \frac{1}{1}\begin{pmatrix} 1 & -1 \\ -1 & 2 \end{pmatrix} \]
Checking:
\[ \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}\begin{pmatrix} 1 & -1 \\ -1 & 2 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \]
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