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Which of the following is true?

a) The product of the eigenvalues of a matrix is equal to the trace of the matrix

b) The eigenvalues of a skew-symmetric matrix are real

c) A is a nonzero column matrix and B is a nonzero row matrix, then the rank of AB is one

d) A system of linear non-homogeneous equations is consistent if and only if the rank of the coefficient matrix is less than or equal to the rank of the augmented matrix

in Linear Algebra by
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1 Answer

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C is true.

Column matrix rank is 1

Row matrix rank is 1

When two matrices are multiplied, the product matrix rank is <= min of the two ranks

Therefore product matrix rank is 1
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