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Let $\mathbb{Z}_2=\mathbb{Z}/2\mathbb{Z}$. Let $\mathrm{GL}_n(\mathbb{Z}_2)$ be the group consisting of all $n\times n$ matrices with entries in $\mathbb{Z}_2$ with non-zero determinant. What is the cohomology algebra $$ H^*(\mathrm{GL}_n(\mathbb{Z}_2);\mathbb{Z}_2)? $$

Could you give any references? Thanks.

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