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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