If \(A^{-1}=\left[\begin{array}{lll}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 5 & 5\end{array}\right]\), then \(A=\)

Let \(\mathrm{A}^{-1} \mathrm{~A}=\mathrm{I}\)
\(
\begin{aligned}
& {\left[\begin{array}{lll}
3 & 2 & 6 \\
1 & 1 & 2 \\
2 & 5 & 5
\end{array}\right] A=\left[\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]} \\
& R_2 \rightarrow 3 R_2-R_1 \text { and } R_3 \rightarrow 3 R_3-2 R_1 \\
& {\left[\begin{array}{ccc}
3 & 2 & 6 \\
0 & 1 & 0 \\
0 & 11 & 3
\end{array}\right] A=\left[\begin{array}{ccc}
1 & 0 & 0 \\
-1 & 3 & 0 \\
-2 & 0 & 3
\end{array}\right]} \\
& R_1 \rightarrow R_1-2 R_2 \text { and } R_3 \rightarrow R_3-11 R_2
\end{aligned}
\)
\(
\begin{aligned}
& {\left[\begin{array}{lll}
3 & 0 & 6 \\
0 & 1 & 0 \\
0 & 0 & 3
\end{array}\right] A=\left[\begin{array}{ccc}
3 & - & 0 \\
-1 & 3 & 0 \\
9 & -33 & 3
\end{array}\right]} \\
& \mathrm{R}_1 \rightarrow \mathrm{R}_1-2 \mathrm{R}_3 \\
& {\left[\begin{array}{lll}
3 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 3
\end{array}\right] \mathrm{A}=\left[\begin{array}{ccc}
-15 & 60 & -6 \\
-1 & 3 & 0 \\
9 & -33 & 3
\end{array}\right]} \\
& \mathrm{R}_1 \rightarrow \frac{1}{3} \mathrm{R}_1 \text { and } \mathrm{R}_3 \rightarrow \frac{1}{3} \mathrm{R}_3 \\
& {\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right] \mathrm{A}=\left[\begin{array}{ccc}
-5 & 20 & -2 \\
-1 & 3 & 0 \\
3 & -11 & 1
\end{array}\right]}
\end{aligned}
\)