= Solution
Grouping by the first <qubit> gives
$$
\frac12\bigl(|00\rangle+|01\rangle+|10\rangle-|11\rangle\bigr)
=\frac{|0\rangle|+\rangle+|1\rangle|-\rangle}{\sqrt2}.
$$
The vectors on both sides form <orthonormal bases>, so this is a <Schmidt decomposition> with two nonzero <Schmidt coefficients> $1/\sqrt2$. Hence \b[the state is maximally entangled]. Independently, its coefficient <matrix> has <determinant>
$$
\det\left[\frac12\begin{pmatrix}1&1\\1&-1\end{pmatrix}\right]=-\frac12\ne0,
$$
which excludes a <product state> by the <two-qubit product-state determinant criterion>. Each <reduced density matrix> is $I/2$.
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