Prove that A is invertable if and only if $a_0 \ne 0$
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
131701
Why is $A^TA$ invertible if $A$ has independent columns?
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
55018
Prove that $A^*A + I$ is invertible
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
141909
Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
70264
Prove that the inverse image of an open set is open
33355
Proving that matrix in equation is invertible
149287
Prove that $A,B>0$ and $A_{ij}0$
151607
Show that  $A\Delta B = C$ if and only if $A = B\Delta C$
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
106585
Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
94855
Prove if a (mod n) has a multiplicative inverse, then it's unique
125195
If matrix A is invertible, is it diagonalizable as well?
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
106398
If $A$ is invertible show that $\det(A) \neq 0$