Proof if $I+AB$ invertible then $I+BA$ invertible and $(I+BA)^{-1}=I-B(I+AB)^{-1}A$
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
3301
If $AB = I$ then $BA = I$
14189
If $(I-A)(I+A)^{-1}$ is orthogonal then prove that A is skew symmetric.
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
25488
Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$