If \( A=\left[\begin{array}{rrr}0 & c & -b \\ -c & 0 & a \\ b & -a ...

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If \( A=\left[\begin{array}{rrr}0 & c & -b \\ -c & 0 & a \\ b & -a & 0\end{array}\right] \) and \( B=\left[\begin{array}{ccc}a^{2} & a b & a c \\ a b & b^{2} & b c \\ a c & b c & c^{2}\end{array}\right] \), show that \( A B=B A=O_{3 \times 3} \).
\( \mathrm{P} \)
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