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Maths-

General

Easy

Question

If A & B are two square matrices such that B = A^–1BA, then (A + B)² equals-

0
A² + B²
A² + 2AB+ B²
A + B

The correct answer is: A² + B²

As B = –A^–1BA
$rightwards double arrow$ AB = –BA $rightwards double arrow$ AB + BA = 0
Now, (A + B)² = A² + BA+ AB + B²
= A² + B²

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