Chapter 6, Problem 29E

If $A=\left[\stackrel{\to }{u}\stackrel{\to }{v}\stackrel{\to }{w}\right]$ is a $3\times 3$ matrix, then the formula $\det \left(A\right)=\stackrel{\to }{v}\cdot \left(\stackrel{\to }{u}\times \stackrel{\to }{w}\right)$ must hold.