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Choose the correct option.
If A and B are two non singular matrices, and AB exists, then (AB)⁻¹ is:
If $A$ and $B$ are two non singular matrices, and $AB$ exists, then $(AB)^{-1}$ is:
- (a)$A^{-1}B^{-1}$
- (b)$B^{-1}A^{-1}$
- (c)$AB$
- (d)None of the above
Answer
Answer
Correct option: (b)
Answer: (b) $B^{-1}A^{-1}$
By the reversal law, $(AB)^{-1}=B^{-1}A^{-1}$, since $(AB)(B^{-1}A^{-1})=AIA^{-1}=I$.