JEE Main 2016MathematicsMatricesMediumMCQ

JEE Main 2016 — Matrices Question with Solution

JEE Main 2016 (10 Apr Online)

Question

Let A, be a 3 ×3 matrix, such that A2-5A+7I=O.
Statement - I : A-1=17 5I-A.
Statement - II : The polynomial A3-2A2-3A+I,can be reduced to 5A-4I. Then :

Choose an option

Show full solutionCorrect option: A
Correct answer
ABoth the statements are true

Step-by-step explanation

A2=5A-7I.....i 

AAA-1-5AA-1-7IA-1=O

AI=5I-7A-1

A-1=17(5I-A)

Hence, the statement I is true.

Now A3-2A2-3A+I

=A5A-7I-2A2-3A+I       {fromi} 

=5A2-7A-2A2-3A+I

=3A2-10A+I

=35A-7I-10A+I       {fromi}

=5A-20I

=5A-4I

Hence, Statement II is true.

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About this question

This is a previous-year question from JEE Main 2016, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.