i don't understand this problem:
Suppose $V$ is a real vector space with $d=\dim V$, $\mathcal{B}:V\times V\rightarrow k$ a nondegenerate symmetric bilinear form. Recall that any symmetric bilinear form extends to a symmetric bilinear form on the exterior algebra $\wedge V$ of $V$ by the formula $$\mathcal{B}\left(v_1\wedge \cdots \wedge v_k, w_1\wedge \cdots \wedge w_k\right)=\operatorname{det}\left(\mathcal{B}\left(v_i,w_j\right)\right).$$