Show that $|I_m-AB|=|I_n-BA|$
12355
Sylvester's determinant identity
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
91829
Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$
120642
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
9574
How to show that $\det(AB) =\det(A) \det(B)$?
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
106322
Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.