# Tagged: binomial expansion

## Problem 587

Let $A$ and $B$ be square matrices such that they commute each other: $AB=BA$.

Assume that $A-B$ is a nilpotent matrix.

Then prove that the eigenvalues of $A$ and $B$ are the same.

Read solution

Add to solve later
Ring theory

by
Yu
· Published 04/02/2017
· Last modified 08/01/2017

## Problem 360

Let $R$ be a commutative ring and let $I_1$ and $I_2$ be **comaximal ideals**. That is, we have

\[I_1+I_2=R.\]

Then show that for any positive integers $m$ and $n$, the ideals $I_1^m$ and $I_2^n$ are comaximal.

Read solution

Add to solve later