Q.2) If $$\mathrm{A}, \mathrm{B}$$ are non-singular square matrices of the same order, then $$\left(A B^{-1}\right)^{-1}=$$
(a) $$A^{-1} B$$
(b) $$A^{-1} B^{-1}$$
(c ) $$B A^{-1}$$
(d) $$A B$$

Answer: (C ) $$B A^{-1}$$
The inverse of a product of matrices $$(X Y)^{-1}$$ is given by the formula $$Y^{-1} X^{-1}$$. In this problem, the matrices are $$A$$ and $$B^{-1}$$.
Applying the formula:
$$
\left(A B^{-1}\right)^{-1}=\left(B^{-1}\right)^{-1} A^{-1}
$$

The inverse of an inverse $$\left(X^{-1}\right)^{-1}$$ is the original matrix $$X$$.
Therefore, $$\left(B^{-1}\right)^{-1}=B$$.
Substituting this back into the equation:
$$
\left(A B^{-1}\right)^{-1}=B A^{-1}
$$

However, the options is $$B A^{-1}$$ as the correct answer option (C )