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A మరియు B అనేది AB = B మరియు BA = A అనే రెండు మాత్రికలు అయితే,  A2 + B2 =?

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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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కాన్సెప్ట్:

మాత్రిక యొక్క అనుబంధ ధర్మము దీని ద్వారా ఇవ్వబడింది:

X (YZ) = (XY) Z      ----(1)

ఇచ్చిన దత్తాంశం:

AB = B మరియు BA = A ----(2)

సాధన:

A2 + B2

AA + BB

⇒ A (BA) + B (AB) [ఉపయోగించి (2)]

(AB) A + (BA) B [ఉపయోగించి (1)]

BA + AB

⇒ A + B

అందువల్ల, A2 + B2 = A + B.

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