MatricesEasy
Question
If the matrices A, B, (A + B) are non-singular (where A and B are of same order), then (A(A+B)-1B)-1 is equal to -
Options
A.A + B
B.A-1 + B-1
C.(A + B)-1
D.AB
Solution
We have (A(A + B)-1B)-1 = B-1((A + B)-1)-1A-1
= B-1(A + B).A-1 = (B-1A + I).A-1
= B-1I + IA-1 = B-1 + A-1
= B-1(A + B).A-1 = (B-1A + I).A-1
= B-1I + IA-1 = B-1 + A-1
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