Matrices and Linear Transformations

Consider the unit square in the app above. If you consider the coordinates of its vertices, listed anticlockwise starting from the origin, you can form the coordinate matrix of the vertices: . Now select a Custom transformation, and set the two elements of the main diagonal of the transformation matrix equal to 2, and the remaining elements equal to 0. What transformation have you obtained? Compare the areas of the unit square and the transformed square. If you set the transformation matrix equal to , what would be the area of the transformed figure? Verify your conjecture by computing the coordinates of the vertices of the transformed figure, and determining its area.

The list of transformations available in the app doesn't include reflection about the origin. Can you obtain this transformation using one of the available options? Explain your answer in detail.