Solution
= Solution
On the line spanned by $n$, $A$ multiplies by $L=\alpha+\beta=a+b+c$. On $n^\perp$, it is the composition of a rotation with a dilation by $r=\sqrt{\alpha^2+\gamma^2}$. Consequently every area in that plane is multiplied by $r^2=\alpha^2+\gamma^2$.