How to prove that if $I+A$ and $I-A$ are nonsingular and $(I−A)(I+A)^{−1}$ is orthogonal then $A$ is skew symmetric?
14189
If $(I-A)(I+A)^{-1}$ is orthogonal then prove that A is skew symmetric.
131611
$A^TA$ is always a symmetric matrix?
52946
If $X$ is an orthogonal matrix, why does $X^TX = I$?
39430
Orthogonal matrix and orthonormal columns
143793
If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
151390
Let $q_1,q_2,q_3,q_4$ be orthonormal vectors in $\mathbb{R}^4$,$z_1,z_2,...,z_6$ orthonormal vectors in $\mathbb{R}^6$ and $A=z_1q_1^T + z_2q_2^T$.
17217
Linear algebra skew symmetric
61538
Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
33030
Proof that $\inf A = -\sup(-A)$
128229
Proving that the transformation obtained from an adjoint pair is natural
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
29230
Orthogonality of Hermite functions
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
111515
Proving that $-a=(-1)\cdot a$
60723
Prove that if $A$ is normal, then eigenvectors corresponding to distinct eigenvalues are necessarily orthogonal (alternative proof)