= Solution
A <parity symmetry in quantum field theory> reverses spatial orientation, so its spatial matrix must lie in the determinant-$-1$ component of the <orthogonal group>. In two spatial dimensions, reversing both coordinates gives $-I_2$, which has determinant $+1$ and is a rotation through $\pi$ in the <special orthogonal group in two dimensions>. It cannot test a discrete orientation-reversing symmetry independent of ordinary rotations. Reflecting one coordinate, for example $\operatorname{diag}(-1,1)$, has determinant $-1$ and supplies the required <parity symmetry in quantum field theory>.
In three spatial dimensions, $-I_3$ has determinant $-1$, so simultaneous inversion of all three coordinates is the standard choice. A single-coordinate reflection also reverses orientation there, and differs from $-I_3$ by a proper rotation through $\pi$. Thus, in a rotationally invariant theory, it tests the same discrete symmetry. The word \i[is] in the source specifies conventional representatives: the essential distinction is orientation reversal, rather than a unique choice of axis. Both transformations preserve the ordinary spatial integration measure through the absolute value of their <Jacobian determinants>.
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