Question

IF $A,B,C$ are non-singular $n\times n$ matrices, then $(ABC{)}^{-1}$ = ____________.

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

Answer 1

The correct option is B $C^{-1}{B}^{-1}{A}^{-1}$

using the property $(AB{)}^{-1}=B^{-1}{A}^{-1}$

$(ABC{)}^{-1}=(BC{)}^{-1}{A}^{-1}=C^{-1}{B}^{-1}{A}^{-1}$

Hence, option B.