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(D) Statement $1$: For any skew-symmetric matrix $A$ of odd order $n$,the determinant $|A| = 0$. Since the order is $5 	imes 5$,$|A| = 0$,which impli

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$4$

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(D) Statement $1$: For any skew-symmetric matrix $A$ of odd order $n$,the determinant $|A| = 0$. Since the order is $5 	imes 5$,$|A| = 0$,which implies $	ext{rank}(A) Statement $2$: If $P$ is a $m 	imes 1$ non-zero column matrix and $Q$ is a $1 	imes n$ non-zero row matrix,then $PQ$ is a $m 	imes n$ matrix of rank $1$. This statement is true.Statement $3$: Let $A = \begin{bmatrix} 1 & 2 & 3 \ 2 & 3 & 4 \ 5 & 6 & 7 \end{bmatrix}$. The determinant $|A| = 1(21-24) - 2(14-20) + 3(12-15) = -3 + 12 - 9 = 0$. Since there exists at least one $2 	imes 2$ minor that is non-zero (e.g.,$\begin{vmatrix} 1 & 2 \ 2 & 3 \end{vmatrix} = -1 
eq 0$),the rank is $2$. This statement is true.Statement $4$: If three distinct lines $a_r x + b_r y + c_r = 0$ are concurrent (intersect at a point),the rows of the matrix are linearly dependent,meaning the determinant is $0$. Thus,the rank must be less than $3$. The statement claiming the rank is $3$ is false.

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