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Simple rotation question

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I know that if I have three 3D vectors (u1,u2,u3), I can create a 3x3 matrix with columns these vectors and if I multiply the inverse of this matrix with a point, actually I transform this point to a system with these three vectors as axes(correct me if I''m wrong). I''d like to know if the same happens with 2D vectors and points. Assume that I have 2 2D vectors(v1,v2) and that I create a 2x2 matrix with columns these 2 vectors. If I multiply a point with the inverse of this matrix, will it happen the same with the above example? And if not, how can I represent this point in a coordinate system with axes the 2 vectors? It''s like I want to change the coordinate system and have as x and y axes the 2 vectors (v1,v2).I hope you understood my question. Thanks!!!

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