The determinant of an nxn matrix A, denoted det(A), is a scalar associated with the matrix A that is defined inductively as
where are the cofactors associated with the entries in the first row of A.
Leon, S. (2010). Linear algebra with applications. Upper Saddle River, NJ: Pearson.
By expanding across the row of all zeros, each term of the cofactor expansion will have a factor of 0. Hence, the sum will equal