Question: How to reduce a matrix?

Here are two matrices:

Ts:=matrix([[cos(omega*t), cos(omega*t-2/3*Pi), cos(omega*t+2/3*Pi)], [sin(omega*t), sin(omega*t-2/3*Pi), sin(omega*t+2/3*Pi)],[1/2, 1/2, 1/2]]);
Xin:=matrix([[cos(omega*t+alpha)],[cos(omega*t+alpha-2/3*Pi)],[cos(omega*t+alpha+2/3*Pi)]]);

Then, if I attempt this operation, 'simplify(multiply(Ts, Xin));', this becomes the result:

Matrix(3, 1, [[cos(omega*t)*cos(omega*t+alpha)+cos(omega*t+(1/3)*Pi)*cos(omega*t+alpha+(1/3)*Pi)+sin(omega*t+(1/6)*Pi)*sin(omega*t+alpha+(1/6)*Pi)], [sin(omega*t)*cos(omega*t+alpha)+sin(omega*t+(1/3)*Pi)*cos(omega*t+alpha+(1/3)*Pi)-cos(omega*t+(1/6)*Pi)*sin(omega*t+alpha+(1/6)*Pi)], [(1/2)*cos(omega*t+alpha)-(1/2)*cos(omega*t+alpha+(1/3)*Pi)-(1/2)*sin(omega*t+alpha+(1/6)*Pi)]])

However, if I attempt to reduce each row, the previous result is reduced much further. 

For example, this shows the expand operation applied to the first row and its result.  

expand(3*cos(alpha)*(1/2)+(1/2)*cos(2*omega*t+alpha)-(1/2)*sin(2*omega*t+(1/6)*Pi+alpha)-(1/2)*cos(2*omega*t+(1/3)*Pi+alpha), trig);
                         

3*cos(alpha)*(1/2)

Is there any way to reduce the entire matrix in a similar way, instead of using this element by element operation?