Answer
$\begin{bmatrix} -13 & 6 & 4 \\ 12 & -5 & -3 \\ -5 & 2& 1 \end{bmatrix}$
Work Step by Step
The general form of a matrix of order $ 3 \times 3$ is:
$\begin{bmatrix} a & b & c \\ d & e & f \\ g & h& i \end{bmatrix}=a(ei-fh) -b(di-fg)+c(dh-eg)$
Now, $det \ A=\begin{bmatrix} 1 & 2 & 2 \\ 3 & 7 & 9 \\ -1 & -4 & -7 \end{bmatrix}=1 (-49+36) - 2 (-21+9)+2 (-12+7)=-23+24=1$
and
$A^{-1}=\dfrac{1}{1} \begin{bmatrix} 1 & 1 & -1 \\ -3 & 2 & -1 \\ 3 & -3 & 2 \end{bmatrix}$
Our answer is: $\begin{bmatrix} -13 & 6 & 4 \\ 12 & -5 & -3 \\ -5 & 2& 1 \end{bmatrix}$
