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If A and B are two matrices such that AB = B and BA = A, then A2 + B2 is equal to

This question was previously asked in
UP TGT Mathematics 2021 Official Paper
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  1. 2AB
  2. 2BA
  3. A + B
  4. AB

Answer (Detailed Solution Below)

Option 3 : A + B
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Detailed Solution

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Concept:

The associative property of matrix is given by:

X (YZ) = (XY) Z      ----(1)

Given:

AB = B and BA = A      ----(2)

Calculation:

A2 + B2

⇒ AA + BB

⇒ A (BA) + B (AB)      [using (2)]

⇒ (AB) A + (BA) B      [using (1)]

⇒ BA + AB

⇒ A + B

Hence, A2 + B2 = A + B.

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