Proof If $AB-I$ Invertible then $BA-I$ invertible.
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
31783
Is this proof of $ab = 0$ correct?
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
50266
In the following figure prove that: $AK||BC$
141173
Are there matrices such that $AB=I$ and $BA \neq I$
35345
How do i prove invertibility of this linear transformation
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
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
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
68724
$||T-I|| < 1$ implies that $T$ is invertible.