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 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 …
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 $3$.
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 …
Matrices - Conditions for $AB+BA=0$ - Mathematics Stack Exchange
There must be something missing since taking $B$ to be the zero matrix will work for any $A$.
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 $b$?
prove $\\Gamma(a)\\Gamma(b) = \\Gamma(a+b)B(a,b)$ using polar ...
Jun 23, 2022 · Are you required to make it wiht polar transformation? Because with the change $x=uv$ $y=u (1-v)$ it's easier
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: …
Integer solutions of $a^b+b^a+1=3ab$ - Mathematics Stack Exchange
Hint: Here you can limit the size of the possible solutions reasonably easily - suppose $a\ge b \gt 3$ then $a^b\gt a^3 \gt 3ab$
$A^2=AB+BA$. Prove that $\\det(AB-BA)=0$ - Mathematics Stack …
I get the trick. Use the fact that matrices "commute under determinants". +1