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Linear algebra Determinants

Let A, B, C,D  Mn(K) with D is invertible. Show that

                     

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Dear everyone!! I would like to share some solution of TD2-Determinant  of Linear algebra with you even you learn from other teacher (keep it as references). 

Solution to TD2-Determinant for some exercises. some questions are still updating. if there is any mistake please kindly correct by yourself. Thank you

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