Question: Simple multiplication of a matrix with another matrix

This gives me an error:

L[2] := `<,>`(`<|>`(1, 0, 0), `<|>`(0, 1, 0), `<|>`(0, 1/4, 1));

L[1] := `<,>`(`<|>`(1, 0, 0), `<|>`(0, 1, 0), `<|>`(-1/2, 0, 1));

P[1] := `<,>`(`<|>`(0, 0, 1), `<|>`(0, 1, 0), `<|>`(1, 0, 0));

P[2] := `<,>`(`<|>`(1, 0, 0), `<|>`(0, 1, 0), `<|>`(0, 0, 1));

A := `<,>`(`<|>`(-2, 7, -2), `<|>`(0, 2, -1), `<|>`(-4, 15, 0));

(L[2]*P[2]*L[1]*P[2])*P[2]*P[1]*A;

dismantle(L[1]);

dismantle(L[2]);

dismantle(P[1]);

dismantle(P[2]);

dismantle(A);

Do I really have to use MatrixMultiply several times now? Does it really have to be that complicated?

(Sorry for the bad formatting, but week after week after week and post after post after post I still don't figure out how to do a simple thing such as paste my 2D-Maple Code in here, I am so disappointed)