How to prove that $I+A^{T}A$ is invertible
55018
Prove that $A^*A + I$ is invertible
152665
$A^TA+I$ is always invertible?
20110
How to prove $(AB)^T=B^T A^T$
30882
Proving Invertibility and Eigenvalues
126018
Show that $ e^{A+B}=e^A e^B$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
146795
Proof If $AB-I$ Invertible then $BA-I$ invertible.
129480
Prove that inf(A+B) = infA + infB
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
33526
How to prove this beautiful statement on linear forms using induction?
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
18282
Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
112707
Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
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 $\det(A)$?
106398
If $A$ is invertible show that $\det(A) \neq 0$
131701
Why is $A^TA$ invertible if $A$ has independent columns?
33355
Proving that matrix in equation is invertible