If and then AB is equal to

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{ccc} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{array}]$ and $B = [\begin{array}{ccc} a^{2} & ab & ac \\ ba & b^{2} & bc \\ ca & cb & c^{2} \end{array}]$ then AB is equal to

none of these

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$A = [\begin{array}{ccc} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{array}]$ and $B = [\begin{array}{ccc} a^{2} & ab & ac \\ ba & b^{2} & bc \\ ca & cb & c^{2} \end{array}]$
Now, $AB = [\begin{array}{ccc} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{array}] [\begin{array}{ccc} a^{2} & ab & ac \\ ba & b^{2} & bc \\ ca & cb & c^{2} \end{array}]$
$\Rightarrow AB = [\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}]$