Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 14

  • Last Updated : 20 Jan, 2020

If A as m×n matrix with rank n, and B as n×p matrix with rank p. Then the rank of matrix C=AB is __________ .
(A) m
(B) n
(C) p
(D) None of these.

Answer: (C)

Explanation: The conditions from the hypothesis imply that m≥n≥p. One knows that,

rank(AB) ≤ min(m,p) = p 

On the other side, from Sylvester Rank Inequality we get,

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

p = n+p−n ≤ rank(AB) 


rank(AB) = p

Option (C) is correct.

Quiz of this Question

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!