If A and B are square matrices and the product is invertible is A necessarily invertible?
158695
Prove that if $AB$ is invertible then $B$ is invertible.
116517
Is every invertible matrix a change of basis matrix?
74460
Matrices A+B=AB implies A commutes with B
71631
About idempotent and invertible matrix
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
61538
Given a square matrix $A$, both $AA^T$ and $A^TA$ are symmetric
101042
Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
130268
How to prove that a nilpotent matrix is not invertible?
139685
If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
78307
Under what conditions is $AA^T$ invertible?
129827
Product of invertibles in $\Bbb Z_n$ [Wilson's Theorem generalization]
24441
Inverse of a matrix is expressible as a polynomial?
108781
$A$ and $B$ are bounded linear operators from the normed linear space $X$ to itself. If $AB$ is invertible are $A$ and $B$ invertible?
39334
Non-degenerate bilinear forms and invertible matrices
42809
How can we show that $(I-A)$ is invertible?
98298
Prove that bilinear form can be presented as product of linear forms if and only if it has rank one