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The rank of a 3 x 3 matrix C = AB found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3 is
  • a)
    1
  • b)
    0
  • c)
    2
  • d)
    3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The rank of a 3 x 3 matrix C = AB found by multiplying a non-zero col...
Note: A nonzero matrix is a matrix that has at least one nonzero element.
Since, det(C) = 0, so rank must be less than 3.
Consider, the 2 x 2 minor of matrix C, again the determinant is zero, so the rank must be less than 2.
The 1 x 1 minor is 1 and determinant of 1 x 1 minor is 1 which is non zero.
the rank of C must be 1.
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