If A= O, such that Ais not equal to I for n belonging to 1 less than equal to n less than equal to 4, then (I-A)-1 equals
1. A
2. A3
3. I+A
4. None of these

Dear Student,
Please find below the solution to the asked query:

We know that when we multiply matrix by its inverse, we get identity matrix.Nowx5-y5=x-yx4+x3y+x2y2+xy3+y4Set y=A and x=I, where Iis identity matrixI5-A5=I-AI4+I3A+I2A2+IA3+A4Given that, A5=0and also In=II-0=I-AI+A+A2+A3+A4I-AI+A+A2+A3+A4=IWe know that when we multiply matrix by its inverse, we get identity matrix.I-AI+A+A2+A3+A4=I-AI-A-1which gives usI-A-1=I+A+A2+A3+A4Hence optionD is correct.

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