Question

Which of the following is not a property of invertible matrices if A and B are matrices of the same order?

(a) (AB)^-1=A^-1 B^-1

(b) (AA^-1)=(A^-1 A)=I

(c) (AB)^-1=B^-1 A^-1

(d) AB=BA=I

I got this question in examination.

I need to ask this question from Invertible Matrices in chapter Matrices of Mathematics – Class 12

Answer 1

The correct answer is (a) (AB)^-1=A^-1 B^-1

Easiest explanation: (AB)^-1=A^-1 B^-1 is incorrect. The correct formula is (AB)^-1=B^-1 A^-1. B^-1 A^-1 ≠ A^-1 B^-1 as matrix multiplication is not commutative.