If A, B and A + B are non singular matrices and AB = BA then 2A - B - A(A + B)-1A + B(A + B)-1B equals
Explanation:
Given, 2A - B - A(A + B)-1A + B(A + B)-1B
= 2A - B - (A + B)-1[A2 - B2]
= 2A - B - (A + B)-1(A - B)(A + B)
= 2A - B - (A + B)-1(A + B)(A - B)
= 2A - B - I(A - B)
= 2A - B - (A - B)
= 2A - B - A + B
= A
Hence, option (a).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.