A) unique solution \[b\,\,\,*\,\,{{a}^{-1}}\]
B) unique solution \[{{a}^{-1}}\,\,*\,\,b\]
C) unique solution \[{{a}^{-1}}\,\,*\,\,{{b}^{-1}}\]
D) many solutions
Correct Answer: A
Solution :
\[x*a=b\Rightarrow (x*a)*{{a}^{-1}}=b*{{a}^{-1}}\] \[\Rightarrow \] \[x*(a*{{a}^{-1}})=b*{{a}^{-1}}\] \[\Rightarrow \] \[x*e=b*{{a}^{-1}}\] \[\Rightarrow \] \[x=b*{{a}^{-1}}\]
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