Question
Question: If the matrices A, B, (A + B) are non-singular, then [A (A + B)<sup>–1</sup> B]<sup>–1</sup>, is eq...
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 of these
Answer
A–1 + B–1
Explanation
Solution
We have
[A (A + B)–1 B]–1 = B–1 ((A + B)–1)–1 A–1
= B–1(A + B)A–1 = (B–1 A + I) A–1
= B–1 I + IA–1 = B–1 + A–1.
Hence (2) is correct answer.