Combining lists with simmilar elements in a matrix (Python)

Question

I have this matrix

mat = [[a, 1], [a, 0, 2], [a, 0, 0, 3],\\
       [b, 1], [b, 0, 2], [b, 0, 0, 3],\\
       [c, 1], [c, 0, 2], [c, 0, 0, 3]]

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