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?
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$A$ is a real orthogonal matrix, prove that $ (I+A)^{-1}(I-A)$ is skew-symmetric
52946
If $X$ is an orthogonal matrix, why does $X^TX = I$?
143793
If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
37794
Proving the two given vectors are orthogonal
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
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Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
133449
A proof that an orthogonal matrix with a determinant 1 is a rotation matrix
28719
Question about Angle-Preserving Operators
134709
Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
107992
Bilinear form with symmetric "perpendicular" relation is either symmetric or skew-symmetric
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
141015
Proof of orthogonal matrix
17217
Linear algebra skew symmetric
84999
$\exp(A)$ is orthogonal iff $A$ is skew symmetric