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## Homework Statement

If A = I + uv*, where u and v are m vectors and A is known to be nonsingular, show that the inverse of A = I + [tex]\alpha[/tex]uv* where [tex]\alpha[/tex] is a scalar value

## Homework Equations

## The Attempt at a Solution

Since A is nonsingular, we know the rank of A is m.

Since both u and v are vectors of dimension m, we know that uv* is a square matrix

From the above statements, we conclude that A is an orthogonal matrix which imples:

A[tex]^{-1}[/tex]

= A [tex]^{*}[/tex]

= (I + uv*)*

= I + (uv*)*

= I + u*v

= I + [tex]\alpha[\tex], since u*v is a scalar value

As you can see, I am arriving at the wrong conclusion. What am I missing? Thank you!