# Homework Help: Inverse Function Theorem

1. Jan 25, 2009

### altcmdesc

1. The problem statement, all variables and given/known data
Prove or Disprove: A 2x2 matrix $$\epsilon A+I$$ has a cube root near $$\left( \begin{array}{cc} 2 & 0 \\ 0 & -5 \end{array} \right)$$.

2. Relevant equations
Inverse Function Theorem

3. The attempt at a solution
I'm just confused about the "near $$\left( \begin{array}{cc} 2 & 0 \\ 0 & -5 \end{array} \right)$$" bit. Is this the matrix $$A$$? Or is it the matrix $$H$$ in the derivative $$Df(A)(H)$$ of the function $$f(A)=A^3$$? Otherwise I know what to do.

Last edited: Jan 25, 2009