If $a^2 = 0$ then $a+1$ and $a-1$ are invertible.
39788
$a+1,a-1$ invertible for nilpotent element
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
13914
If $a^2+b^2=c^2$ then $a$ or $b$ is even.
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
134075
Inverse of $A^{-1}+B^{-1}$
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
5729
If $a^2+b^2+c^2=1$ then prove the following.
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
78307
Under what conditions is $AA^T$ invertible?
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
152665
$A^TA+I$ is always invertible?
131701
Why is $A^TA$ invertible if $A$ has independent columns?
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
19909
if $abc=1$, then $a^2+b^2+c^2\ge a+b+c$
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C