Hey guys quick simple question I'm having some troubles with,

Define and where is non-zero. Suppose

Show that no matrix exists such that

Trivially if B is a 0 matrix then the above is self-evident. it's in situations when it is not 0 that i am having trouble. Bellow is an example where this is true,

and

But since there is no inverse of B we cannot have

So I have one case where this is true but I can't see the connection in a general sense. I suppose we need to show that any matrix B that satisfies the above doesnt have an inverse.