Question
Question: If A & B are two square matrices such that B = A<sup>–1</sup>BA, then (A + B)<sup>2</sup> equals-...
If A & B are two square matrices such that
B = A–1BA, then (A + B)2 equals-
A
0
B
A2 + B2
C
A2 + 2AB+ B2
D
A + B
Answer
A2 + B2
Explanation
Solution
As B = –A–1BA
Ž AB = –BA Ž AB + BA = 0
Now, (A + B)2 = A2 + BA+ AB + B2
= A2 + B2