JEE Main 2015MathematicsMatricesEasyMCQ

JEE Main 2015 — Matrices Question with Solution

JEE Main 2015 (04 Apr)

Question

If A=12221-2a2b is a matrix satisfying the equation AAT=9I , where I is 3×3 identity matrix, then the ordered pair a, b is equal to 

Choose an option

Show full solutionCorrect option: A
Correct answer
A-2, -1

Step-by-step explanation

Given, A A T =9I

12221−2a2b12a2122-2b=9I

⇒90a+4+2b092a+2−2ba+4+2b2a+2−2ba2+4+b2=900090009

Equation a+4+2b=0 ⇒a+2b=−4  ...1

2a+2−2b=0 ⇒2a−2b=−2  ...2    

&  a2+4+b2=9⇒a2+b2=5  ...3     

On solving, we get  a=−2, b=−1

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About this question

This is a previous-year question from JEE Main 2015, 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.