Properties of Matrix-vector Product

• $A$ and $B$ are m*n matrices, $u$ and $v$ are vectors in $R^n$,and c is a scalar.
• $A(u+v)= Au+Av$
• $A(cu)= c(Au)=(cA)u$
• $(A+B)u=Au+Bu$
• $AO$ is the m*1 zero vector
• $Ov$ is also the m*1 zero vector
• $I_nv=v$
• $A$ and $B$ are m*n matrices. If $Aw=Bw$ for all $w$ in $R^n$.Is it true that $A=B$? Yheah