Question A.4: Consider the matrix A = |1 2 3 4 5 6 3 1 2| Its adjoint is A......
Consider the matrix
\overline{A}=\left|\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 1 & 2 \end{matrix} \right|
Its adjoint is
\overline{A}_{adj}=\left|\begin{matrix} 4 & -1 & -3 \\ 10 & -7& 6 \\ -11 & 5 & -3 \end{matrix} \right|
and the determinant of \overline{A} is equal to -9.
Step-by-Step
Thus, the inverse of \overline{A} is
\overline{A}^{-1}=\left|\begin{matrix} -\frac{4}{9} & \frac{1}{9} & \frac{1}{3} \\\\ -\frac{10}{9} & \frac{7}{9} & -\frac{2}{3} \\\\ \frac{11}{9} & -\frac{5}{9} & \frac{1}{3} \end{matrix} \right|
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