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Exercise:
Gl_nK owed with matrix multiplication ABmapsto A B is a group. The unity is I_n. The inverse of Ain textGL_nK is A^-. Moreover forall ABin textGL_nK we have: A^-^-A AB^-B^-A^-

Solution:
Proof. Let ABin textGL_nK. We first need to show that ABin textGL_nK too. Indeed B^- A^-ABB^-A^-ABB^-I_nBB^-BI_n and ABB^- A^-ABB^-A^-AI_nA^-AA^-I_n The other statements in the proposition follow immediately from what we have proven earlier.
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Exercise:
Gl_nK owed with matrix multiplication ABmapsto A B is a group. The unity is I_n. The inverse of Ain textGL_nK is A^-. Moreover forall ABin textGL_nK we have: A^-^-A AB^-B^-A^-

Solution:
Proof. Let ABin textGL_nK. We first need to show that ABin textGL_nK too. Indeed B^- A^-ABB^-A^-ABB^-I_nBB^-BI_n and ABB^- A^-ABB^-A^-AI_nA^-AA^-I_n The other statements in the proposition follow immediately from what we have proven earlier.
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eth, hs22, lineare algebra, proof
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