Given two square matrix matrices ($A$ and $B$ both have the same order) such that $AB = I$ is it true that $BA=I$?
3301
If $AB = I$ then $BA = I$
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
82410
Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
37061
The order of $ab$ when $a,b$ commute
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
105921
Why do we have $ab=ba$?
34973
Is it true that the order of $ab$ is always equal to the order of $ba$?
49409
Are all of the following statements equivalent? (vectors and matrices)
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
147490
If matrix $AB=A$, does it mean B must be an identity matrix?
27767
Are two matrices similar iff they have the same Jordan Canonical form?
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
145980
For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?
66709
Are the matrix products $AB$ and $BA$ similar?
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.