if $AA^*$ = $A + A^*$ then $A$ is normal
43913
Prove that if $A^*+A=AA^*$ then $A$ is normal
30356
$a =\prod_{i = 1}^{r} p_{i}^{ai}$ with $a_{i} > 0$ for each $i$ is the canonical representation of $a$...
67784
If $A + A^t = 2I$ then $\det(A) \geq 1$
78997
If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.
150024
Is a*b* regular?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
145397
How to prove that for every $i$, $a_i = i$
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
152665
$A^TA+I$ is always invertible?
89175
Proof of $(a+b)^{n+1}$
84535
The spectral radius of normal operator
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
150320
Why does $a^{b}·a^{c}=a^{b+c}$?
38095
The Commutator Subgroup is Normal.
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.