Site navigation

If \(A, B\) and \(A + B\) are non singular matrices and \(AB = BA\) then \(2A - B - A(A + B)^{-1}A + B(A + B)^{-1} B\) equals

Question and options

If A,BA, B and A+BA + B are non singular matrices and AB=BAAB = BA then 2A−B−A(A+B)−1A+B(A+B)−1B2A - B - A(A + B)^{-1}A + B(A + B)^{-1} B equals
  1. A
  2. B
  3. A + B
  4. I

Answer and explanation

Correct answer: A - A
Since A,B commute, (A+B)^-1 commutes with both, so A(A+B)^-1A - B(A+B)^-1B = (A^2-B^2)(A+B)^-1 = (A-B)(A+B)(A+B)^-1 = A-B. Expression = 2A-B-(A-B) = A.

Practice for these exams

  • IPMAT Indore

Related question papers

Related exam syllabi

More solved explanations in Arithmetic