\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Verify bilinearity on a small example: with \(A = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}\), \(B = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}\), \(C = \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}\), compute \((A + B) C\) on one hand and \(A C + B C\) on the other, and check they agree.
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