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Matrix with negative indices

Is there a way or hack to operate with matrices with negative indices? For example a 3x3 matrix with row indices {-1,0,1} and column indices {-1, 0, 1}. So one can do m[-1,-1] for first row and column entry, while still retain matrix operations (ring ops, determinant, etc.). I'm dealing with random walks where the symetry needs that.