How to prove that $(M\mathbf {a} )\times (M\mathbf {b} )=(\det M)M^{-T}(\mathbf {a} \times \mathbf {b} )$?

Question

In computer vision, there are lots of formula came in being with geometry form. And this equation is very about Fundamental matrix in epipole geometry. So, can some one proof this equation? $${\displaystyle (M\mathbf {a} )\times (M\mathbf {b} )=(\det M)\left(M^{-1}\right)^{\mathrm {T} }(\mathbf {a} \times \mathbf {b} )=\operatorname {cof} M(\mathbf {a} \times \mathbf {b} )}$$