= Solution
\b[False.] The counterexample just given is antisymmetric in every basis and has zero contraction with every <symmetric second-rank tensor>. It still fails the <Cartesian second-rank tensor> transformation law, because its value is nonzero in one basis and zero in another. Thus \b[antisymmetry alone, together with symmetric tests, proves no tensor transformation law]. The same <blindness of symmetric contraction tests to antisymmetric arrays> applies even when the array is assumed antisymmetric.
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