  Every quasigroup $(S,\cdot)$ belongs to a set of 6 quasigroups, called
parastrophes denoted by $(S,\pi_i)$, $i\in \{1,2,3,4,5,6\}$. It is shown that
isotopy-isomorphy is a necessary and sufficient condition for any two distinct
quasigroups $(S,\pi_i)$ and $(S,\pi_j)$, $i,j\in \{1,2,3,4,5,6\}$ to be
parastrophic invariant relative to the associative law. In addition, a
necessary and sufficient condition for any two distinct quasigroups $(S,\pi_i)$
and $(S,\pi_j)$, $i,j\in \{1,2,3,4,5,6\}$ to be parastrophic invariance under
the associative law is either if the $\pi_i$-parastrophe of $H$ is equivalent
to the $\pi_i$-parastrophe of the holomorph of the $\pi_i$-parastrophe of $S$
or if the $\pi_i$-parastrophe of $H$ is equivalent to the $\pi_k$-parastrophe
of the $\pi_i$-parastrophe of the holomorph of the $\pi_i$-parastrophe of $S$,
for a particular $k\in \{1,2,3,4,5,6\}$.
