Calculation and analysis: How to verify if Laguerre polynomials are orthogonal?

I have the problem of checking if the Laguerre polynomials for n = 1, …, 10 are orthogonal.

I have to create the list of these polynomials, then create the array of integrals from 0 to infinity. Something like:

M = Integrate[LaguerreL[i,x] Laguerre[j,x] Exp[-x]{x, 0, infinity}] 

And in the end I have to draw the dynamic drawing of these polynomials so that if I choose in the graph n, from 0 to 20, the correct polynomial will be drawn with its derivative.