Let f be a function on R^p to R^p which is differentiable on a neighborhood of a point c and suc

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Step 1: Since $Df(c)$ has an inverse, it is invertible. This means that $Df(c)$ is a square matr

Let $f$ be a function on $\mathrm{R}^p$ to $\mathrm{R}^p$ which is differentiable on a neighborhood of a point $c$ and such that $D f(c)$ has an inverse. Then is it true that $f$ has an inverse on a neighborhood of $c$ ?