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Question:
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$$
\text { If } A=\left[\begin{array}{ccc}
0 & c & -b \\
-c & 0 & a \\
b & -a & 0
\end{array}\right] \text { and } B=\left[\begin{array}{ccc}
a^2 & a b & a c \\
a b & b^2 & b c \\
a c & b c & c^2
\end{array}\right] \text {, }
$$
then $A B$ is equal to
Options:
\text { If } A=\left[\begin{array}{ccc}
0 & c & -b \\
-c & 0 & a \\
b & -a & 0
\end{array}\right] \text { 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] \text {, }
$$
then $A B$ is equal to
Solution:
1863 Upvotes
Verified Answer
The correct answer is:
O
O
$\begin{aligned} &\quad A B=\left[\begin{array}{ccc}0 & c & -b \\ -c & 0 & a \\ b & -a & 0\end{array}\right]\left[\begin{array}{ccc}a^2 & a b & a c \\ a b & b^2 & b c \\ a c & b c & c^2\end{array}\right] \\ & A B=\left[\begin{array}{ccc}a b c-a b c & b^2 c-b^2 c & b c^2-b c^2 \\ -a^2 c+a^2 c & -a b c+a b c & -a c+a c \\ a^2 b-a^2 b & a b^2-a b^2 & a b c-a b c\end{array}\right] \\ & =\left[\begin{array}{lll}0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right]=\mathrm{O} \\ & \end{aligned}$
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