Let A be a 3 × 3 matrix such that a d j a d j a d j . A = 12 4 . Then A - 1 a d j   A is equal to

Let A be a 3×3 matrix such that adjadjadj.A=124. Then A-1adj A is equal to
  1. 23
  2. 6
  3. 12
  4. 1

Solution

Given equation is

adjadjadj.A=124

⇒A(n-1)3=124

∵ n=3

⇒A(3-1)3=124

⇒A8=124

⇒A2=12

⇒A=23

Now, A-1adj A=A-1.adj A=1A×A3-1

=A=23

Asked in: JEE Main 2023 (24 Jan Shift 2)

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