Question

lf $A=\left[\begin{array}{ccc}o& c& -b\\ -c& o& a\\ b& -a& o\end{array}\right]and$ $B=\left[\begin{array}{ccc}{a}^2& ab& ac\\ ab& b^2& bc\\ ac& bc& c^2\end{array}\right],$ then $AB=$

• A. $A$
• B. $B$
• C. $I$
• D. $O$

Answer 1

The correct option is D $O$

Multiplying the two matrices we get,

$\left[\begin{array}{ccc}0+abc-abc& 0+c{b}^2-c{b}^2& 0+b{c}^2-b{c}^2\\ -a^{2}c+0+a^{2}c& -abc+0+abc& -a{c}^2+0+a{c}^2\\ a^{2}b-a^{2}b+0& a{b}^2-a{b}^2+0& abc-abc+0\end{array}\right]$

$=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$

$=O$

Hence the answer is option D