5. (20%) Let D be the differentiation operator on the set of all polynomials of degree less than 3, and D is defined as follows:

$$D(p(x)) = xp'(x) + p''(x).$$

Now define the matrix A representing D with respect to $$[1, x, x^2]$$ and the matrix B representing D with respect to $$[1, x, 1+x^2]$$. Show that the matrix A and the matrix B are similar to each other.