Let V be a m dimensional vector space over real numbers.
A be a linear operator on V,
\wedge^{p}A be a linear operator on p-th exterior algebra \wedge^{p}V,as defined by
(\wedge^{p}A)(v_{1}\wedge...\wedge v_{p})=(Av_{1})\wedge...\wedge(Av_{p}).
D^{p}A is another linear operator, as defined by
(D^{p}A)(v_{1}\wedge...\wedge v_{p})=\sum_{r=1}^{p}v_{1}\wedge...\wedge v_{r-1}\wedge(Av_{r})\wedge v_{r+1}\wedge...\wedge v_{p}.
v_{1},...,v_{p}\in V.
We difine \wedge^{0}A be the identity endomorphism,
D^{0}A be the zero endomorphism of the scalars.

how can we get the formula?
det(I-e^{xA})=\sum_{p=0}^{m}(-1)^{p}Tr(\wedge^{p}( e^{xA}))=\sum_{p=0}^{m}(-1)^{p}Tr(e^{xD^{p}A})