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Symbolic Manipulation of Matrices [Newbie Question]


Hello,
I am a complete newbie in Mathematica and wante to solve the following:

I have the matrix Y and the vector P0.
The vector P1 = Y.PO
Now I transform P1 to Star.
This expresses Star in term of Y.PO.

I would like to know now how can I simplify this expression so it yields
Star = Ytransformed * P0.

I can do that by hand, but I wonder how do such things in Mathematica

Thanks for any pointers!
Best,
Stefan



Y = {{Subscript[y, 11], Subscript[y, 12]}, {Subscript[y, 21],
   Subscript[y, 22]}}

P0 = {Subscript[p0, 1], Subscript[p0, 2]}

P1 = Y.P0

Star = {P1[[1]] + (1 - a)*P1[[2]], a*P1[[2]]}



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