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 Nov15 comment $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible. This is how I did the problem the first time, but then I forgot how I did it and was stuck. :P Thanks :-) Nov15 comment $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible. Thank you for another nice answer. Nov15 comment $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible. Thank You. It makes the proof quite obvious now. :D Nov14 comment Is this $SL_3(\mathbb{F_2})$ look like? @sos440 +1 for the complete list Nov3 comment How many decimal places are needed for incremental average calculation? @JernejJerin If you are satisfied with the answers, you might consider accepting them, else you might want to indicate what more information you want. Oct29 comment Good problem book on Abstract Algebra I unaccepted your answer and instead accepted Dedalus's answer since on retrospective, I have found some of the book Exercise in Algebra and other books a more concentrated source of problems. I hope you don't mind. Oct26 comment Determinant of a Modified Jacobian of a Function That's all there to it?! I came up with a similar but infinitely cruder solution, however, I was not sure of this. Also, I was thinking there might be some rank-related solution also. Anyway, thanks. :-) Oct18 comment How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$ @vesszabo No, he uses it in this direction, but goes upto infinity, however, I am not sure of the formal justification of the step. Oct18 comment How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$ The logic is similar to $\sqrt{x-5} =5 \implies \sqrt{x-\sqrt{x-5}} = 5$ Sep28 comment Cycling Digits puzzle Added some more explanation. I hope it is more clear now. Sep28 comment Cycling Digits puzzle @PerManne Yup. Sorry about that, I was going to update it. Sep26 comment field generated by a set Where I mean $K$ by $G_{S}$ Sep26 comment field generated by a set @JasonDeVito I guess your objection is invalid, since we are talking about $S$ generating $R$, rather than $S$ being $R$ itself. Since, if $\frac{1}{10} \in S$ then $\frac{k}{10} \in G_{S}$ where $k \in Z$. Sep26 comment field generated by a set @FortuonPaendrag You say that your proof is flawed. I think it would be good if you can probably indicate why do you think it is flawed in the answer itself. Sep25 comment In what spaces does the Bolzano-Weierstrass theorem hold? @KevinCarlson Its okay. I do not mind. Sep25 comment In what spaces does the Bolzano-Weierstrass theorem hold? I guess not. So, basically, we want to find conditions for total boundedness and completeness from the metric of the space and the set of points? Is this true? Sep25 comment In what spaces does the Bolzano-Weierstrass theorem hold? @KevinCarlson Okay. If I say that total boundedness of a closed subspace of a complete metric space implies compactness and vice-versa. Will that address the question enough? Sep22 comment How to Find a Finite-Difference Matrix You might want to learn more about the finite difference methods. I am sure there are enough textbooks on the same that explain the process in detail. Sep22 comment Non surjectivity of the exponential map to GL(2,R) Try $A = \left(\matrix{1 & 0 \\ 0 & -2}\right)$. And show that this cannot be an exponential, since exponential cannot be negative in $\mathbb{R}$. Sep20 comment Sequence of convex functions @LVK Okay.Thanks.