Question

let ABC be a well-defined product of matrices. suppose that A,C are both invertible. Prove that rank(ABC) = rank (b)

Answer 1

Like does this have to do with A^TA cancels out??

Answer 2

so A and C are invertible (And hence square)
lets say A is a n x n matrix
and C is a m x m matrix
so we know that rank(A) = n and rank(C) = m

and B have to be a matrix of n x m since ABC is a well defined product

now can you use this fact :
Rank(AB) = Rank(B)
(it works in our case since A is rank n and B itself is n x m)
?

Answer 3

by can you use it i ask if you know it and we dont have to prove it also

Answer 4

I guess you managed to do it?