Consider the following square with the four corners and the center marked as $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$ and $\mathrm{T}$ respectively.
Let $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ represent the following operations:
$\mathrm{X}$ : rotation of the square by $180$ degree with respect to the $\mathrm{S}-\mathrm{Q}$ axis.
Y: rotation of the square by $180$ degree with respect to the $\text{P-R}$ axis.
$\mathrm{Z}$ : rotation of the square by $90$ degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point $T$.
Consider the following three distinct sequences of operation (which are applied in the left to right order).
- $\text{XYZZ}$
- $\text{XY}$
- $\mathrm{ZZZZ}$
Which one of the following statements is correct as per the information provided above?
- The sequence of operations $(1)$ and $(2)$ are equivalent
- The sequence of operations $(1)$ and $(3)$ are equivalent
- The sequence of operations $(2)$ and $(3)$ are equivalent
- The sequence of operations $(1)$, $(2)$ and $(3)$ are equivalent
