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Surabhi posted an Question
July 03, 2020 • 21:10 pm 30 points
  • IIT JAM
  • Mathematics (MA)

1.64. let a and b be real n xn matrices such that ab + b2 is non-singular. then (i) a is non-singular but a +b is singular (ii) both a and a + b are non-singula

1.64. Let A and B be real n Xn matrices such that AB + B2 is non-singular. Then (i) A is non-singular but A +B is singular (ii) both A and A + B are non-singular ii) both B and A + B are non-singular (iv) both A and B are non-singular.

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    Ujjawal vishal best-answer

    Given, |AB+B^2|≠0 (since , AB +B^2 is nonsingular). => |B(A+B)|≠0 => |B||A+B|≠0 So, B ≠0 or ,|A+B|≠0 hence option iii is true.

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