Discussion
A matrix is said to be of rank zero if and only if :
Answer: D
A matrix has rank zero if and only if all its elements are zero.
The rank is the largest number of linearly independent rows (or columns), equivalently the order of the largest non-vanishing minor. Any single non-zero element is itself a non-vanishing 1 by 1 minor, giving rank at least 1. So rank 0 means every element is zero: the null matrix.
A zero determinant with non-zero elements only says the rank is less than full. A matrix equal to its own inverse is invertible and has full rank, and a matrix with zero diagonal can still have full rank.
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