JEE Main 2019 Mathematics question
Let A and B be two invertible matrices of order 3 × 3. If det(ABA) = 8 and det(AB) = 8, then det(BAB) is equal to:
Answer: (C)
Solution
|A||B| = 8 and |A|/|B| = 8 ⇒ |B| = 1/2, |A| = 4; required = |B|/|A| = 1/16.
Let A and B be two invertible matrices of order 3 × 3. If det(ABA) = 8 and det(AB) = 8, then det(BAB) is equal to:
|A||B| = 8 and |A|/|B| = 8 ⇒ |B| = 1/2, |A| = 4; required = |B|/|A| = 1/16.