Why is invertible matrix defined in the current way
3301
If $AB = I$ then $BA = I$
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
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 $\det(A)$?
86919
When (and more importantly, why) does $AA^T$ have an inverse?
35834
Is the product of any two invertible diagonalizable matrices diagonalizable?
111769
Why is inverse of orthogonal matrix is its transpose?
143629
Looking for insightful explanation as to why right inverse equals left inverse for square invertible  matrices
46567
Derivatives of inverse matrix
67498
Intuition behind the definition of linear transformation
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
83903
Why transforming normals with the transpose of the inverse of the modelview matrix?
21571
Why are real symmetric matrices diagonalizable?
25229
Can any set of $n$ relatively prime elements be extended to an invertible matrix?
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
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
66995
Why is a projection matrix symmetric?