Show that there is a symmetric matrix A such that $\forall g\in G,\rho(g)^tA\rho(g)=A$.
58595
Existence of a G-invariant matrix
110200
Determinant of a Special Symmetric Matrix
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
144145
Symmetric $3\times 3$ Matrices - Base matrix
79055
Orders of a symmetric group
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
100845
How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
18012
Eigenvectors of real symmetric matrices are orthogonal
157806
Order of a element on a Symmetric Group
55493
Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
99346
Prove a result on transitive group actions.
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
21217
$G$, group. $a,b\in G$. Show that $|a|=|a^{-1}|; |ab|=|ba|$, and $|a|=|cac^{-1}|, \forall c\in G$.
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
90845
Is this posible in GR $g_{ab}g^{ab}=1$?
21568
Maximal order of an element in a symmetric group