Prove that sum of 2 simple bivectors in $R^{4}$ is not necessarily a simple bivector

Question

Prove that sum of 2 simple bivectors in $R^{4}$ and other higher dimensional spaces is not necessarily a simple bivector and show that $B^{2}$ is not a scalar?

I want to show that $B$ does not have a specific property of a bivector.
note: $B=e_1 \land e_2 +e_3 \land e_4$.
I am having problems figuring this out

Answer 1

$$B^2 = BB = (e_1\wedge e_2 + e_3 \wedge e_4)(e_1\wedge e_2 + e_3 \wedge e_4) = (e_1e_2 + e_3e_4)(e_1e_2 + e_3e_4) \\ = e_1e_2e_1e_2 + e_1e_2e_3e_4 + e_3e_4e_1e_2 + e_3e_4e_3e_4 = -1+I+I-1= -2+2I$$ which is not a scalar. Thus $B$ cannot be a simple bivector (i.e. $2$-blade).