Why does a shear matrix work only with x-axis or y-axis invariance?

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Why can't a typical shear matrix work for invariant oblique lines? I understand that shearing a plane figure in 2D is essentially the mapping of points proportional to their perpendicular distance from the invariant line, and that the shear matrix is multiplied with the coordinate matrix of a plane figure to shear it with an invariant line with a shear factor of $n$ where $n\in\mathbb{R}$. However, what I do not understand is that, why this general form of the shear matrix in the image attached below (I am not able to attach images to my post), does not work for oblique invariant lines.

Any help is appreciated, please!