Linear transformations with the same kernel If two linear transformations between finite-dimensional vector spaces, we say
$$L,T : V \longrightarrow W$$
has the same kernel, and kernel is not the space zero. Is $T$ a multiple of $L$?

Hint:  Take square matrices of order $2$ like $A=[a_{ij}]$ where $a_{11}=1, a_{12}=a_{21}=a_{22}=0$ and $B=[b_{ij}]$ where $b_{21}=1, b_{11}=b_{12}=b_{22}=0$ 
