# Geometric interpretation of transformation matrices

$\vec e A = \vec e \frac{1}{3}\left(\begin{array}{ccc}-2&1&1\\1&-2&1\\1&1&-2\end{array}\right)$
I tried changing it to another basis, $\vec f = \vec e \left(\begin{array}{ccc}1&-2&1\\1&1&-2\\1&1&1\end{array}\right)$, and got this matrix instead: $B = \left(\begin{array}{ccc}0&0&0\\0&-1&0\\0&0&-1\end{array}\right)$