If $ABBA-BAAB=A-B$, show $\operatorname {tr} …
Jan 26, 2026 · That is, there seems to be fairly strong symbolic evidence that for $n=4$, if $ABBA-BAAB = A-B$ and $A$ is nilpotent, then $B^4 = \lambda I$ for some $\lambda$.
How to calculate total combinations for AABB and ABBB sets?
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 ways: …
How many ways can we get 2 a's and 2 b's from aabb?
Because abab is the same as aabb. I was how to solve these problems with the blank slot method, i.e. _ _ _ _. If I do this manually, it's clear to me the answer is 6, aabb abab abba baba bbaa baab Which is …
CW complex for Möbius strip and its homeomorfisams
Jan 14, 2023 · According to this question, there is CW complex with one 0-cell,one 1-cell and one 2-cell. No such CW structure exists on the the Möbius strip. Moreover the linked question doesn't claim that, …
random variables - probability of playing music player on shuffle and ...
1.How many sequences of 4 songs are there where no song plays twice in a row? If we label the songs {A, B, C, D}, then examples are ABCD and ABAB but not ABBA. For this problem I just thought the …
elementary number theory - Divisibility Tests for Palindromes ...
I've found and proven the following extensions to palindromes of the usual divisibility rules for 3 and 9: A palindrome is divisible by 27 if and only if its digit sum is. A palindrome is divisible by 81 if and only if …
How many $4$-digit palindromes are divisible by $3$?
Feb 28, 2018 · Hint: in digits the number is $abba$ with $2 (a+b)$ divisible by $3$.
matrices - string function - Mathematics Stack Exchange
Jane loves string more than anything. She made a function related to the string some days ago and forgot about it. She is now confused about calculating the value of this function. She has a str...
$A^2=AB+BA$. Prove that $\det (AB-BA)=0$ [duplicate]
I get the trick. Use the fact that matrices "commute under determinants". +1
If $ab+ba=1$ and $a^3=a$ in a ring, show that $a^2=1$.
Sep 19, 2023 · The first condition holds for all $b$ or for some particular $b$?