Is there a systematic way of counting the number of invertible matrices in a general linear group with entries in a finite ring? For example, GL(3, Z_2). The determinant has to be zero, but other than that, I don't know any systematic way of counting them. I usually start by saying that there are at least 13 non-invertible ones (if at least one row or column are zeros) then I look at the equation of the determinant and try to go from there.(adsbygoogle = window.adsbygoogle || []).push({});

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# Invertible Matrix

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