Question
Question: If A and B are two square matrices such that B = –A<sup>–1</sup> BA, then (A + B)<sup>2</sup> is equ...
If A and B are two square matrices such that B = –A–1 BA, then (A + B)2 is equal to –
A
0
B
A2 + B2
C
A2 + 2AB + B2
D
A + B
Answer
A2 + B2
Explanation
Solution
As B = –A–1 BA, we get AB = –BA or AB + BA = O
Now, (A + B)2 = (A + B) (A + B)
= A2 + BA + AB + B2
= A2 + O + B2
= A2 + B2