- #1

daniel_i_l

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## Homework Statement

A and B are nxn matricies. B =/= 0 and rank(A)=n-1

Prove or disprove that:

1) if AB=0 then rank(B)=1

2) if BA=0 then rank(B)=1

## Homework Equations

## The Attempt at a Solution

If n=2 and we define A as:

[1 1]

[1 1]

and B as:

[1 -1

[-1 1]

then rank(A) = 1 = 2-1 and B=/=0 but AB=BA=0 and rank(B)=2 whick disproves both (1) and (2). Is that right? It seems odd that they'd give to similar questions with identical answers.