= Cubically invariant second-rank tensor
{title2=$A=aI$}
A <Cartesian second-rank tensor> in three dimensions invariant under quarter-turn <rotations> about all three coordinate axes is a scalar multiple of the <identity matrix>. Squaring the quarter-turns gives coordinate half-turns; invariance under these forces every off-diagonal component to vanish. The quarter-turns then equate the three diagonal components. This conclusion does not require the original <tensor> to be symmetric.
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