Let $A$ be a matrix, and let $B$ be the result of doing a row operation to $A$. Show that the null space of $A$ is the same as the null space of $B$. Let $A$ be a matrix, and let $B$ be the result of doing a row operation to $A$. Show that the null space of $A$ is the same as the null space of $B$.  
Any ideas of what I can do to show this? If the null spaces have to be equal then the vector $x$ in $Ax=0$ and $Bx=0$ have to be equal, but how can I show that $B$ is the result of doing a row operation to $A$ and that $A$ and $B$ are equal?

Let $P$ be the matrix corresponding to the row operation performed.
We define the null space as the set L= $\left\{\vec{x} \in \mathbb{F}^n |\space A\vec{x} = 0\right\}$
 So, for any vector $\vec{x}\in L $ for $B$ we have: $B\vec{x}=PA\vec{x}=\vec{0}$
We work in the exact same manner for a vector in the null space of $B$, say $L'$ to show $L=L'$.
