Really interesting. So, I thought that maybe inv could be redefined as
(;:^._1).
But all I get is:

inv_z_=.(;:^._1)

|domain error

| inv_z_=.( ;:^._1)

t=:*(;:^._1)

|domain error

| t=:*( ;:^._1)

(;:^._1)

|domain error

| ( ;:^._1)
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