Question

If for the non-singular matrix A, A2 = I, then find A-1.
(a) A
(6) I
(c) O
(d) None of these

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Answer 1

$\rm :\implies\: {A}^{2} = I$

$\pink{ \tt \: Pre \: multiply \: by \: {A}^{ - 1} \: on \: both \: sides}$

$\rm :\implies\: {A}^{ - 1} {A}^{2} = {A}^{ - 1} I$

$\rm :\implies\:A = {A}^{ - 1}$

$\rm \: \boxed{ \pink{ \bf \: Hence, \: option \: (a) \: is \: correct\: \tt \: }}$