\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) and \(B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\). Show that for every \((\alpha, \beta) \in \mathbb{R}^2\), \(\alpha A + \beta B\) is the zero matrix if and only if \(\alpha = \beta = 0\).
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