and 
then \[10{{A}^{-1}}\] is equal to [JEE MAIN Held on 08-01-2020 Evening]
A) \[6l-A\]
B) \[4l-A\]
C) \[A-4l\]
D) \[A-6l\]
Correct Answer: D
Solution :
\[\because \] Every square matrix satisfying characteristic equation \[\Rightarrow \,\,\,\,\,\,\,\,\left| A-\lambda I \right|=0\] 
\[\Rightarrow \,\,\,\,\,\,\left( \lambda -4 \right)\left( \lambda -2 \right)=18\] \[\Rightarrow \,\,\,\,\,\,{{\lambda }^{2}}-6\lambda -10=0\] \[\therefore \,\,\,\,\,\,{{A}^{2}}-6A-10I=0\] (By Pre multiplication of \[{{A}^{-1}}\] both sides) \[\Rightarrow \,\,\,\,\,\,A-6I=10{{A}^{-1}}\]
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