$T$:$R^2{R}^3,S$:$R^3{R}^4$ be linear transtormation defined by $T(x,y)=(x+2y,3x,-2y)$

$S(x,yz)=(2z-x,y+3x,4z,5y)$

Find $S*T$:$R^2{R}^4,m(S),m(T),m(S*T)$ with respect to standard basis of $R^2,R^3,R^4.$Verify $m(S*T)=m(S)m(T)$