A) \[5A+I\]
B) 5A + 21
C) \[5A+3I\]
D) \[5A+4I\]
Correct Answer: C
Solution :
Given, \[{{A}^{2}}=A+I\] Thus, \[{{A}^{5}}={{A}^{2}}.\,{{A}^{2}}A\] \[=(A+I)\,(A+I)A\] \[=({{A}^{2}}+2AI+{{I}^{2}})A\] \[=(A+I+2A+I)A\] \[=(3A+2I)A\] \[=3{{A}^{2}}+2IA\] \[=3(A+I)+2IA\] \[=3A+3I+2A\] \[=5A+3I\]You need to login to perform this action.
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