How to multiply matrices and then get the inverse?

I am trying to multiply two matrices and then calculate the inverse of the result matrix in J. My matrix looks like this:

   x =: i. 2 3
0 1 2 
3 4 5
   y =: i. 3 2
0 1
2 3
4 5

What is the set of commands I would use to multiply these two together and then calculate the inverse?

And if the matric does not have the inverse, what are the commands to deal with that problem?

Solution

Elvex has identified the relevant operations above, you can combine them to multiply matrix x by matrix y and find the inverse as follows:

   %. x +/ .* y
  1.11111 _0.361111
_0.777778  0.277778