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If every minor of order ‘r’ of a matrix is zero then ρ (A) =?

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If every minor of order ‘r’ of a matrix is zero then ρ (A) =?

(a) >r

(b) =r

(c) ≤r

(d) <r

I have been asked this question in homework.

I need to ask this question from Finding Inverse and Rank of Matrix topic in portion Matrices of Engineering Mathematics

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The correct option is (d) <r

For explanation: By the definition of ‘Rank of a matrix’

A matrix is said to have rank ‘r’ if

(i) At least one minor of order r is non-zero

(ii) All minors of order r+1 is zero

∴ The given matrix (ii) condition seems to be applied

Hence, rank of matrix ρ (A) = < r.

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