# Math Help - A proof of cross product and det

1. ## A proof of cross product and det

Prove that $|a \ \times \ b |^2 = det \left(\begin{array}{cc}(a \cdot a)&(a \cdot b)\\(a \cdot b)&(b \cdot b)\end{array}\right)$

So far I have $det \left(\begin{array}{cc}(a \cdot a)&(a \cdot b)\\(a \cdot b)&(b \cdot b)\end{array}\right) = (a \cdot a) \cdot (b \cdot b) - (a \cdot b) \cdot (a \cdot b)$

But I don't know how the cross product would look like after calculation. Hints?

2. I think I got it.

I just used the properties of dot product and cross product.