If $A,B$ are $n\times n$ matrices and we have that $AB= I_n$, why do we need to show that $BA=I_n$ as well to show that $A$ is an inverse of $B$?
3301
If $AB = I$ then $BA = I$
72092
If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
140252
Matrices - Conditions for $AB+BA=0$
66709
Are the matrix products $AB$ and $BA$ similar?
77554
Inverse of the sum of matrices
123044
Commutative matrices are multiples of the identity
141173
Are there matrices such that $AB=I$ and $BA \neq I$
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
113474
An $n \times n$ matrix $M$ of integers has the property that $M_{ab} = M_{xy}$ iff $a+b=x+y$. How many distinct elements are there in $M$?
141922
Reason for reversing the order when transpose and inverse of a group of matrices
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
77941
If A, B, C, D are non-invertible $n \times n$ matrices, is it true that their $2n \times 2n$ block matrix is non-invertible?
105921
Why do we have $ab=ba$?
52040
"Inverse" of an $n\times k$ matrix.
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?