How to prove that if $AB=I$（$I$ is the identity matrix), both the $n^{th}$ order matrices $A$ and $B$ are invertible?
3301
If $AB = I$ then $BA = I$
109217
Invertibility of the Product of Two Matrices
83178
Matrix Group induction proof and order of elements question
75066
If the product of two square matrices is invertible, then both matrices are invertible
70157
Is every matrix $A$ such that $A^k=I$ diagonalizable?
9574
How to show that $\det(AB) =\det(A) \det(B)$?
4517
Showing a $2\times2$ matrix is invertible
37252
How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$?
33355
Proving that matrix in equation is invertible
158695
Prove that if $AB$ is invertible then $B$ is invertible.
152665
$A^TA+I$ is always invertible?
131701
Why is $A^TA$ invertible if $A$ has independent columns?
153506
Proving the inverse of a matrix equals $I_n-\frac{1}{n-1}A$
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
61868
Prove that $ND = DN$ where $D$ is a diagonalizable and $N$ is a nilpotent matrix.
127127
Prove condition number of a invertible matrix is atleast one