If A = 1 2 2 2 1 - 2 a 2 b is a matrix satisfying the equation A A T = 9 I , where I   is 3 × 3…

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 

  1. -2, -1
  2. 2, -1
  3. -2, 1
  4. 2, 1

Solution

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

Asked in: JEE Main 2015 (04 Apr)

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