If $A,B$ are invertible, show that $AB$ is invertible and express $(AB)^{-1}$ in terms of $A^{-1},B^{-1} $.
109217
Invertibility of the Product of Two Matrices
90402
$AB$ is not invertible
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
158862
Show that $a(-1) = (-1)a = -a $.
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
30882
Proving Invertibility and Eigenvalues
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
10042
How to Show that Linear transformation is invertible?
76610
Show that $f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
53113
$I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$