Understand the problem Let A be a 3 x 3 real matrix with all the diagoanl entries equal to 0 . If 1 + i is an eigen value of A , the determinant of A equal ? Source of the problem Sample Questions (MMA ) :2019 Topic Linear Algebra Difficulty Level Medium Suggested...

Understand the problem The number of rings of order 4, up to isomorphism, is:(a) 1(b) 2(c) 3(d) 4. Source of the problem TIFR GS 2018 Part B Problem 12 Topic Abstract Algebra Difficulty Level Easy Suggested Book Dummit and Foote Start with hints Hint 0Hint 1Hint 2Hint...

Understand the problem What are the last 3 digits of (2^{2017})?(a) 072(b) 472(c) 512(d) 912. Source of the problem TIFR GS 2018 Part B Problem 9 Topic Number theory Difficulty Level Easy Suggested Book Burton Start with hints Hint 0Hint 1Hint 2Hint 3 Do you really...

Understand the problem Let G be a finite group and g ∈ G an element of even order. Then wecan colour the elements of G with two colours in such a way that x andgx have different colours for each x ∈ G. Source of the problem TIFR GS 2018 Part A Problem 24 Topic...

Understand the problem If (alpha) is a root of (x^2) – x +1 = 0 , then (alpha^{2018}) + (alpha^{-2018}) is Source of the problem Sample Questions (MMA) : 2019 Topic Quadratic Roots Difficulty Level Medium Suggested Book Abstract Algebra – Dummit and...

Understand the problem A countable group can have only countably many distinct subgroups. Source of the problem TIFR GS 2018 Part A Problem 21 Topic Group Theory Difficulty Level Easy Suggested Book Abstract Algebra, Dummit and Foote Start with hints Hint 0Hint 1Hint...