ISRO 2010-ECE matrices

Question

If every minor of order 'r' of a matrix 'A' is zero, then rank of 'A' is

a) greater than 'r'
b) equal to 'r'
c) less than or equal to 'r'
d) less than 'r'

Answer 1

d because there is no determinent of size greate than equal r to whose det is not zero

Answer 2

Given an m × n matrix with real entries (or entries from any other field) and rank r, then there exists at least one non-zero r × r minor, while all larger minors are zero. Hence answer is option D.