Let a be an M * n matrix and B be an n * m matrix. It is proved that when m > N, there must be | ab | = 0

Let a be an M * n matrix and B be an n * m matrix. It is proved that when m > N, there must be | ab | = 0

Because R (AB)

If the matrix AB = e, then the determinant | a | B | = | e | why?
Why are determinants on both sides of an equation equal

AB = e means that AB is the inverse of each other, that is, B = a ^ (- 1)
So: | a | B | = | a | a ^ (- 1)|
So obviously the conclusion is true

Let a be an irreversible matrix of order n, and prove the existence of a nonzero matrix of order n such that ab = CA = 0

(1) A is irreversible, so its rank is less than N, so it can be changed into a matrix DD = (PK). (P2) (P1) a = QA through finite row elementary transformations P1, P2,. PK. Let q = (PK). (P2) (P1) take F as such a matrix: the elements in the first row, the first column are: 1, and the other elements are: 0. Then there is FD = 0, that is, FQA = 0