GATE 2002 CS question 1.1 (Matrix Algebra)

1.1 The rank of the matrix

1	1
0	0

is:
(a) 4 (b) 2 (c) 1 (d) 0

What's this 'rank' of a matrix? Well, it's the count of how many rows of the matrix can stand independently. What that means is: how many rows there are such that they cannot be formed just by multiplying other rows by something and adding them up.
Here, it is obvious that the second row can be obtained by multiplying the first row by 0. So, the rank is 1.
Another, maybe clearer, way to arrive at the same answer is: the row rank of any matrix (what we found above) is equal to its column rank. Here, we see that the two columns are equal. So, the second column is 'dependent' on the first column (or you may take it the reverse way). Either way, there's only one 'independent' column, hence the column rank is 1.
Here the answer is (c) 1