For any skew-symmetric matrix $K$, if $(I-K)$ is invertible, show that $B=(I+K)(I-K)^{-1}$ satisfies $B^tB=I=BB^t$.
15417
Tricky problem on skew-symmetric matrices
4517
Showing a $2\times2$ matrix is invertible
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
13026
Prove that if AB=I_m, then rk(A)=rk(B).
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
119301
Is the following matrix invertible?
146438
Determinant of a special skew-symmetric matrix
75215
Properties of invertible matrices
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
24441
Inverse of a matrix is expressible as a polynomial?
86246
Basis for Skew Symmetric Matrix
74460
Matrices A+B=AB implies A commutes with B
17217
Linear algebra skew symmetric
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
150715
Prove that the determinant of skew-symmetric matrices of odd order is zero
130268
How to prove that a nilpotent matrix is not invertible?