Nov 21, 2013 · Truly lost here, I know abba could look anything like 1221 or even 9999. However how do I prove 11 divides all of the possiblities?

Aug 29, 2013 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …

Jan 11, 2015 · there is a similar thread here Coordinate-free proof of $\operatorname {Tr} (AB)=\operatorname {Tr} (BA)$?, but I'm only looking for a simple linear algebra proof.

You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …

For example a palindrome of length $4$ is always divisible by $11$ because palindromes of length $4$ are in the form of: $$\\overline{abba}$$ so it is equal to $$1001a+110b$$ and …

Let $A,B$ be two $3\times 3$ matrices with complex entries, such that $A^2=AB+BA$. Prove that $\det (AB-BA)=0$

Oct 14, 2018 · I could easily prove this using 2x2 matrices and multiplying them together, but how do you generally prove this and using letters not matrices? (this isn't homework, we haven't …

Apr 19, 2022 · Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB...), where order matters and repetition is allowed, both can be rearranged in different …

Feb 28, 2018 · How many $4$-digit palindromes are divisible by $3$? I'm trying to figure this one out. I know that if a number is divisible by $3$, then the sum of its digits is divisible by $3$. All I …

Dec 11, 2014 · Prove that $a^a \\ b^b \\ge a^b \\ b^a$, if both $a$ and $b$ are positive.