Question
Question: If the matrices A, B , (A + B) are non singular then [A (A + B)<sup>–1</sup> B]<sup>–1</sup> is equ...
If the matrices A, B , (A + B) are non singular then
[A (A + B)–1 B]–1 is equal to –
A
A + B
B
A–1 + B–1
C
A (A + B)–1
D
None
Answer
A–1 + B–1
Explanation
Solution
B–1 ((A+B)–1)–1 A–1 = B–1 (A +B) A–1
= (B–1 A + B–1 B) A–1 = (B–1 A + I ) A–1
= B–1 AA–1 + IA–1
= B–1 + A–1