In a non-zero matrix $A$, the rank $r$ means that
Aevery minor of order $r$ is zero
Bthere exists at least one non-zero minor of order $r$, and every minor of order greater than $r$ is zero
Call minors of every order are non-zero
Dthe determinant of $A$ is non-zero
Answer & Solution
Correct answer: B. there exists at least one non-zero minor of order $r$, and every minor of order greater than $r$ is zero
The rank is the highest order of a non-zero minor. So at least one minor of order $r$ must be non-zero, while all minors of order greater than $r$ must vanish. That is exactly option B.
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