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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