Gravitation By Charles Misner, Kip Thorene, John Wheeler page 129.
The components of the exterior product of $p$ vectors
$\displaystyle (\cal u_1\wedge u_2\wedge...\wedge u_p)^{\alpha_1...\alpha_p} =... =p!u_1^{[\alpha_1}u_2^{\alpha_2}...u_p^{\alpha_p]} =\delta^{\alpha_1\alpha_2...\alpha_p}_{1,2...p}\det[(u_\mu)^\lambda]$
Some related information could be found here. Determinant and Levi-Civita symbol But still, I'm a bit confused of why exterior product could be so closely connected to determinant.
Is it because Levi-Civita symbol could be computed from the determinate of Kronecker delta? Does this carry any further implications?
(A related reference could be found here: Product of Levi-Civita symbol is determinant? where guestDiego's answer provided some insights.)