gate 2014

Question

Two matrices A and B are given below:

A=

p	q
r	s

 B=

p2 + q2	pr + qs
pr +qs	r2 + s2

If the rank of matrix A is N, then the rank of matrix B is

•  
   (A) N /2
•  
   (B) N-1
•  
   (C)  N
•  
   (D) 2 N

 

Answer 1

 MAtrix B is the product of A and A^T(transpose of A).

RANK(AA^T) =RANK(A)

so RANK(B)= N = answer?(c).

for reference to theorem follow the link :

https://math.stackexchange.com/questions/215145/rank-of-product-of-a-matrix-and-its-transpose