Question

If A and B are square matrices and $A^{-1}$ and $B^{-1}$ of the same order exist, then $(AB{)}^{-1}$ is equal to :

• A. $A{B}^{-1}$
• B. $A^{-1}B$
• C. $A^{-1}{B}^{-1}$
• D. $B^{-1}{A}^{-1}$

Answer 1

Answer: (D)

Let A and B be square matrices and $A^{-1},B^{-1}$ be of same order.
then $(AB{)}^{-1}=B^{-1}.A^{-1}$.