Prove that if $I-BA$ is invertible then $I-AB$ is invertible
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
65432
Prove that every elementary matrix is invertible, and the inverse is again an elementary matrix.
94383
Prove that $A^TD-C^TB=I$
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
75215
Properties of invertible matrices
35345
How do i prove invertibility of this linear transformation
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
152104
How do I prove that $ij = k?$
30882
Proving Invertibility and Eigenvalues
78298
On the nilpotence of the matrix $AB-BA$
130268
How to prove that a nilpotent matrix is not invertible?
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
7034
Prove that $A+I$ is invertible if $A$ is nilpotent