- #1
chocolatefrog
- 12
- 0
Proof involving nonsingular matrices.
If (I + A) is nonsingular, prove that (I - A)(I + A)-1 = (I + A)-1(I - A), and hence (I - A)/(I + A) is defined for the matrix.
I've proved it like this:
Let (I - A)(I + A)-1 = A, and (I + A)-1(I - A) = B.
B-1 = (I - A)-1(I + A)
B-1A = I
Premultiplying by B, we get A = B.
Is this proof correct?
Homework Statement
If (I + A) is nonsingular, prove that (I - A)(I + A)-1 = (I + A)-1(I - A), and hence (I - A)/(I + A) is defined for the matrix.
I've proved it like this:
Let (I - A)(I + A)-1 = A, and (I + A)-1(I - A) = B.
B-1 = (I - A)-1(I + A)
B-1A = I
Premultiplying by B, we get A = B.
Is this proof correct?
Last edited: