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If ${\left\{ {\left( \begin{gathered}
3\,\,1\,\,2 \hfill \\
8\,\,9\,\,5 \hfill \\
1\,\,\,1\,\,3 \hfill \\
\end{gathered} \right)\,\left( \begin{gathered}
1\,\,3\,\,3 \hfill \\
3\,\,2\,\,7 \hfill \\
3\,\,7\,\,9 \hfill \\
\end{gathered} \right)\left( \begin{gathered}
3\,\,8\,\,1 \hfill \\
1\,\,\,9\,\,1 \hfill \\
2\,\,5\,\,3 \hfill \\
\end{gathered} \right)} \right\}^2}\, = \,\left( \begin{gathered}
a_1\,\,a_2\,\,a_3 \hfill \\
b_1\,\,b_2\,\,b_3 \hfill \\
c_1\,\,c_2\,\,c_3 \hfill \\
\end{gathered} \right)$
then the value of $|a_2 - b_1| + |a_3 - c_1| + |b_3 - c_2|$ is
$0$
$1$
$2$
$3$
Solution
$\mathrm{x}=\left(\mathrm{ABA}^{\mathrm{T}}\right)^{2}\{\mathrm{B} \text { is symmetric }\}$
$\mathrm{X}^{\mathrm{T}}=\mathrm{X} \Rightarrow \mathrm{B}^{2}$ symmetric hence required value
$=0$
