For non-singular square matrix A, B and C of the same order
Question:

For non-singular square matrix $A, B$ and $C$ of the same order $\left(A B^{-1} C\right)=$

(a) $A^{-1} B C^{-1}$

(b) $C^{-1} B^{-1} A^{-1}$

(c) $C B A^{-1}$

(d) $C^{-1} B A^{-1}$

Solution:

Disclaimer: In Quesion, We are to find the inverse of $\left(A B^{-1} C\right)$. The inverse is missing in the question.

(d) $C^{-1} B A^{-1}$

We have,

$\left(A B^{-1} C\right)^{-1}=C^{-1}\left(B^{-1}\right)^{-1} A^{-1}$

$=C^{-1} B A^{-1}$