Please submit your concern

Question:

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).