Question

Alternating multilinear map properties to calculate determinet

Answer 1

Answer:

f any component xi of an alternating multilinear map is replaced by xi + c xj for any j ≠ i and c in the base ring R, then the value of that map is not changed.

Every alternating multilinear map is antisymmetric.

If n! is a unit in the base ring R, then every antisymmetric n-multilinear form is alternating.

Explanation: