rajtendulkar

Dear Forum,

I have one question on matrix multiplication.

Suppose there are 2 matrices -

A = 1 -1 0
0 2 -1
2 0 -1

B = 1
1
2

and AB = 0 (Zero Matrix)
if B not a zero-matrix, then rank(A) is less than s, where s is the dimension of B.

I wanted to have a proof and explanation for this.
Any book / link? :)

Thank You,
Raj