= Solution
The first index of the printed <Levi-Civita symbol> is fixed at $1$. Thus the matrix in the first <orthonormal basis> is
$$
A=I+(\epsilon_{1ij})=\begin{pmatrix}1&0&0\\0&1&1\\0&-1&1\end{pmatrix},
\qquad \det A=2.
$$
The specified matrix in the other basis is $I$, with <determinant> one. If this array were a <Cartesian second-rank tensor>, an orthogonal basis change would give $A'=RAR^T$, and
$$
\det A'=(\det R)^2\det A=\det A.
$$
The determinants disagree, proving \b[the array is not a tensor]. The fixed index matters: the TeX aid drops it, but the original PDF clearly prints $\epsilon_{1ij}$.
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