Proof that $(AA^{-1}=I) \Rightarrow (AA^{-1} = A^{-1}A)$
3301
If $AB = I$ then $BA = I$
104424
If each eigenvalueof $A$ is either $+1$ or $-1$ $ \Rightarrow$ $A$ is similar to ${A^{ - 1}}$
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
108633
Why $f^{-1}(f(A)) \not= A$
145397
How to prove that for every $i$, $a_i = i$
55018
Prove that $A^*A + I$ is invertible
107824
Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian
119387
If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
43913
Prove that if $A^*+A=AA^*$ then $A$ is normal
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
111515
Proving that $-a=(-1)\cdot a$
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
55094
How to show $i^{-1} = -i$?
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
31783
Is this proof of $ab = 0$ correct?
95057
Possible fake proof of $1= -1$