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Rank of adj mAtrix

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4 4 votes

Here Rank of A = 2

1 2 3 4
0 1 2 3
0 0 0 0
0 0 0 0

Here n =4.

There are three conditions to decide adj of matrix.

rank of the adjoint matrix is :
n if r(A)=n
1 if r(A)=n-1
0 if r(A)<n-1

Our case falls into 3rd condition. r(A) =2, n =4 hence r(A) <n-1

Hence r(adj(A)) = 0

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