Question

求证（t*a）*b=t*(a*b)=a*(t*b)

Answer 1

I suppose a,b are vector, t is scaler

let a, b be nth dimensional vector

a = (x1,x2,.,xn)

b = (y1,y2,.,yn)

(ta).b = (tx1,tx2,.,txn).(y1,y2,yn)

= t(x1y1+x2y2+..+xnyn)

a.(tb) = (x1,x2,..,xn). ( (ty1,ty2,.,tyn)

= t(x1y1+x2y2+...+xnyn) = (ta).