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Regard a 2 x 2 matrix A as a topological space by considering 2x2 matrices as vectors (a,b,c,d) as a member ofR^{4}. Let GL_{2}(R) cR^{4}be the subset of the 2x2 matrices A which are invertible, i.e. such that ad does not equal bc.

Consider the following, giving reasons:

(i) Is GL_{2}(R) cR^{4}an open subspace?

(ii) Is GL_{2}(R) compact?

(iii) Is GL_{2}(R) connected?

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# Matrices as topological spaces

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