Vector Notation: Division and Order Reversal

Question

Let vectors $a=(x,y,z)$, $b=(z,y,x)$, $c=(1/x,1/y,1/z)$;

How do we write $b$ and $c$ in term of $a$? Which notation shall we use? Can we say:

$c=1/a$?

Let Matrix $A=(1,2;3,4)$, how to write matrix $B=(2,1;4,3)$ in term of $A$?

I found the solution to the last question and the operation to get $b$: it is $b=Ja$ where $a$ is a column vector, $J$ is the anti-diagonal identity matrix.

Also, $B=AJ$

Answer 1

c=1/a is pretty nonstandard notation - you can use index notation: $c_i=\frac{1}{a_i}$

As for b, I'm not aware of any standard notation for that - writing it out in full is probably best