$\left[ {\begin{array}{*{20}{c}}
1&2&2\\
2&1&{ - 2}\\
a&2&b
\end{array}} \right]\left[ {\begin{array}{*{20}{r}}
1&2&{\rm{a}}\\
2&1&2\\
2&{ - 2}&b
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
9&0&0\\
0&9&0\\
0&0&9
\end{array}} \right]$
${{\rm{a}} + 4 + 2{\rm{b}} = 0 \Rightarrow {\rm{a}} + 2{\rm{b}} = - 4}$ ......$(i)$
${2{\rm{a}} + 2 - 2{\rm{b}} = 0 \Rightarrow {\rm{a}} + 2{\rm{b}} = - 1}$ .......$(ii)$
${{\rm{ From (i) and (ii) }}}$
${3{\rm{b}} = - 3 \Rightarrow {\rm{b}} = - 1}$
${{\rm{a}} = - 2}$
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