Hey guys,

can anyone help me with this problem please ??

Given A be m * n (m by n) matrix and B be n * p (n by p) matrix

Show that 1. rank(AB) is less than or equal to rank(A)

2. rank(AB) is less than or equal to rank(B)

3. If B is invertible, than rank(AB) = rank(A)

i think 1 and 2 are kind of similar ? so clear explanation on 1 and 3 are appreciated. Thanks so much!!