# how can we prove that the subset of all invertible matrices is open? [duplicate]

Possible Duplicate:
Why do the $n \times n$ non-singular matrices form an “open” set?

Consider the space of all nxn matrices with real entries with the standard metric, i.e.,view the matrix as an element of $R^{n^2}$and use the usual Euclidean metric on $R^{n^2}$. I need to prove that the subset of all invertible matrices is open. Please any idea?

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## marked as duplicate by Zev ChonolesFeb 18 '12 at 6:40

$\bf Hint:$ $A$ is invertible iff the determinant is different from zero.