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AAaA(aA)-1=1a A-1, where a is any real number and A is a square matrix. - Mathematics

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Question

`("aA")^-1 = 1/"a"  "A"^-1`, where a is any real number and A is a square matrix.

Options

  • True

  • False

MCQ
True or False
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Solution

This statement is True.

Explanation:

If A is a non-singular square matrix, then for any non-zero scalar ‘a‘, aA is invertible.

∴ `("aA") * (1/"a" "A"^-1) = "a" * 1/"a" * "A" * "A"^-1` = I

So, (aA) is inverse of `(1/"a" "A"^-1)`

⇒ `("aA")^-1 = 1/"a" "A"^-1`

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Chapter 4: Determinants - Exercise [Page 84]

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NCERT Exemplar Mathematics [English] Class 12
Chapter 4 Determinants
Exercise | Q 49 | Page 84

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