A) \[nA-(n-l)I\]
B) \[nA-I\]
C) \[{{2}^{n-l}}A-(n-I)I\]
D) \[{{2}^{n-l}}A-I\]
Correct Answer: A
Solution :
As we have \[{{A}^{2}}=2A-I\] \[\Rightarrow \,\,{{A}^{2}}A\,=(2A-I)\,A=2{{A}^{2}}-IA\] \[\Rightarrow \,{{A}^{3}}=2(2A-I)\,-IA=3A-2I\] Similarly, \[{{A}^{4}}\,=4A-3I\] \[{{A}^{5}}=5A-4I\] ???????.. ???????.. ???????.. Hence, \[{{A}^{n}}\,=nA\,-(n-1)I\]You need to login to perform this action.
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