$A$ is a singular matrix of order five. $B$ is another matrix having the $\operatorname{rank} \rho(B)$ equal to the rank $\rho(A)$ and $B$ has a non-zero minor of order 3. Then which one of the following is true?

• A

  $B$ is a $4 \times 4$ matrix
• B

  $\rho(A)=\rho(B)=4$, irrespective of the order of $B$
• Correct answer
  C

  $\rho(A)=\rho(B)=3$, when all the fourth order minors of $A$ are zero
• D

  $|B|=0$

Hence, the correct answer is option: 'C'.