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Question Number 55770 by Joel578 last updated on 04/Mar/19

Let A and B are matrices in R^(2017×2017)  that satisfy  A^(−1)  = (A + B)^(−1)  − B^(−1)   and  det(A^(−1) ) = 2017  Find   det(B)

$$\mathrm{Let}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{matrices}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2017}×\mathrm{2017}} \:\mathrm{that}\:\mathrm{satisfy} \\ $$$${A}^{−\mathrm{1}} \:=\:\left({A}\:+\:{B}\right)^{−\mathrm{1}} \:−\:{B}^{−\mathrm{1}} \\ $$$$\mathrm{and} \\ $$$$\mathrm{det}\left({A}^{−\mathrm{1}} \right)\:=\:\mathrm{2017} \\ $$$$\mathrm{Find}\:\:\:\mathrm{det}\left({B}\right) \\ $$

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