= Solution
Represent each point by a nonzero column $v_i$. The source's <cross-ratio> is
$$
\frac{\det(v_1,v_3)\det(v_2,v_4)}{\det(v_1,v_4)\det(v_2,v_3)}.
$$
Rescaling representatives cancels between numerator and denominator. If the <projective transformation> is represented by $A\in\operatorname{GL}_2(\mathbb C)$, then $\det(Av_i,Av_j)=\det(A)\det(v_i,v_j)$. Two factors of $\det(A)$ occur in both numerator and denominator and cancel. Hence \b[the <cross-ratio> is invariant under every <projective transformation>].
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