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If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to -

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Question

If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to

Options

  • A

  • 1 – A

  • 1

  • 3A

MCQ

Solution

1

Explanation:

(I + A)3 – 7A = I3 + A3 + 3I2A + 3A2I – 7A

= 1 + A3 + 3A + 3A2 – 7A

= 1 + A2, A + 3A + 3A – 7A

= 1 + A, A – A

= 1 + A2 – A

= 1 + A – A = 1

∴ (1 + A)3 – 7A = 1

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