Chapter A.3, Problem 3P

In each of Problems 1 through 10, use elementary row and column operations to simplify the task of evaluating the determinant by cofactor expansions. If $\text{A}$ is nonsingular, find ${\text{A}}^{-1}$.

$\text{A}\text{=}\left(\begin{array}{ccc}1& 2& 3\\ 2& 4& 5\\ 3& 5& 6\end{array}\right)$