The skew-symmetric matrix of order 5×5, has rank less than 5 because determinant of odd ordered skew symmetric matrix is zero. If P is a non-zero column matrix and Q is a non-zero row matrix, then PQ is a matrix of order 1×1, so rank of matrix PQ is one. Since, the
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|=1(21−24)−2(14−20)+3(12−15)
=−3+12−9=0 and there is no cofactor of any elements is zero, so rank is 2. If the lines arx+bry+cr=0,(r=1,2,3) are distinct and intersect at a point, then matrix