The product of matrix (AB)-1A is
The product of matrix (AB)-1A is
- A.
AB-1A
- B.
ABA-1
- C.
A-1
- D.
B-1
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Correct answer: D
Key idea: use the rule for the inverse of a product: (AB)^{-1} = B^{-1} A^{-1}.
Start with (AB)^{-1} A and replace (AB)^{-1} by B^{-1} A^{-1}:
This gives B^{-1} A^{-1} A.
Use A^{-1} A = I to simplify to B^{-1} I = B^{-1}.
Conclusion: (AB)^{-1} A = B^{-1}.