- #1
alingy1
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Show that if A, B and A+B are invertible matrices with the same size, then
$$A(A^{-1}+B^{-1})B(A+B)^{-1}=I$$
What does the result in the first part tell you about the matrix $$(A^{-1}+B^{-1})$$?
I get the first part. Help me with the second part. My book says that the matrix $$(A^{-1}+B^{-1})$$ is not equal to $$(A+B)^{-1}$$
How did they mathematically prove that?
$$A(A^{-1}+B^{-1})B(A+B)^{-1}=I$$
What does the result in the first part tell you about the matrix $$(A^{-1}+B^{-1})$$?
I get the first part. Help me with the second part. My book says that the matrix $$(A^{-1}+B^{-1})$$ is not equal to $$(A+B)^{-1}$$
How did they mathematically prove that?