# On the definition of the lineality of a polyhedron

Consider a Polyhedron defined by the linear inequality $Ax\leq b$ where $A$ is a matrix, and $b$ is a vector.

I've seen the following definition of the lineality of $P$ : $Lin(P)$ is the kernel of $A$.

My question is : since $A$ is not unique in the description of $P$, is there a simple proof that this definition actually makes sense, that is to say, that $Ker A$ is actually independent of the choice of $A$ in the description of $P$ ?