proof: $A-A(A+B)^{-1}A=B-B(A+B)^{-1}B$
60006
Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
127293
Prove that $(a-b) \mid (a^n-b^n)$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
9986
Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
111515
Proving that $-a=(-1)\cdot a$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
80009
Prove that $| |a|-|b| | \le |a-b|$
65923
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
150320
Why does $a^{b}·a^{c}=a^{b+c}$?
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
153295
Algebraic Identity $a^{n}-b^{n} = (a-b) \sum\limits_{k=0}^{n-1} a^{k}b^{n-1-k}$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
24856
Proving sup(A + B) = sup A + sup B
33030
Proof that $\inf A = -\sup(-A)$
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.