matrix algebra

IIT JEE 2015 Preparation › Algebra questions › matrix algebra

If A² - A+ I =0 then the inverse of A is

1. A+I
2.A
3.A-I
4.I-A

#Mathematics #Algebra

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2 Answers

saikat_iit2012sa SAMANTA ·2011-07-01 06:50:27

A²-A+I=0
MULTIPLYING THROUGHOUT BY A^-1

A²A^-1-AA^-1=-IA^-1

NOW AS A²A^-1 IS EQUAL TO A BY THE PROPERTY OF MATRIX....AND AA^-1 IS EQUAL TO I AND -IA^-1 IS EQUAL TO -A^-1...SO THE FINAL ANSWER CAME TO BE A^-1 IS EQUAL TO

A-I=-A^-1

SO A^-1 EQUALS

I-A

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vatsal singh ·2011-07-22 11:04:51

I am also getting the same answer.

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