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This is stated without proof in dummit and foote. Instead, you can save this post to reference later. G is a generalized inverse of a if and only if aga=a.g is said to be reflexive if and only if gag=g

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I was trying to solve the problem What's reputation and how do i get it If a is a matrix and g be it's generalized inverse then g is reflexive if and only if rank (a)=rank (g).

We have a group $g$ where $a$ is an element of $g$

Then we have a set $z (a) = \ {g\in g Ga = ag\}$ called the centralizer of $a$ If i have an $x\in z (a)$, how. To gain full voting privileges,

Prove that $\forall u,v\in g$, $uv\sim vu$ My confusion lies in the fact that they appear to be the same question I'm sure i must be wrong, but my approach was to again show that $\sim$ is an equivalence relation. $1) $$ (gag^ {-1})^ {-1}=g^ {-1^ {-1}}a^ {-1}g^ {-1}=ga^ {-1}g^ {-1}$ $2)$ $ ga (g^ {-1}g)bg^ {-1}=g (ab)g^ {-1}$ I'm stuck at this point, Is it correct so far? is.