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Let $A = (a_{ij}) ∈M_n(\mathbb{R})$; $n≥3$. Let $B = (b_{ij})$ be the matrix of its co- factors, i.e. $b_{ij}$ is the cofactor of the entry $a_{ij}$ in $A$. What is the rank of $B$ when
a. the rank of $A$ is $n$?
b. the rank of $A$ is less than, or equal to, $n ≥ 2$?

I am completely stuck on it.how can i solve this.

  • 0
    For b. the rank of $A$ is _always_ less than or equal to $n$, so what do you mean here?2012-12-29
  • 0
    Part b should be: the rank of $A$ is less than or equal to $n-1$2012-12-29

2 Answers 2