If $A=\large\frac{1}{3}$$\begin{bmatrix} 2 & 2 & 1 \\-2 & 1 & 2 \\1 & -2 & 2 \end{bmatrix}$ prove that $A^{-1}=A^T$.

Question

\[\begin{array} {1 1}(1) u \; is \; a \; unit \; vector & (2) \overrightarrow{u}=\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\\(3)\overrightarrow{u}=\overrightarrow{0}& (4) \overrightarrow{u}\neq \overrightarrow{0}\end{array}\]