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If A is an invertible matrix of order n and k is any positive real number, then the value of [ det (k A)]⁻¹ det A is

Options

  1. Ak ^ - n
  2. Bk ⁻¹
  3. Ck ^ n
  4. Dnk

Correct answer

A. k ^ - n

Step-by-step solution

If A is matrix that is invertible then det- ( kA ) will be k ^ n . det ( A ) , where n is the order. aligned & [ det ( KA )]⁻¹ det ( ~A ) & = [( K )^ n det ( A ) ]⁻¹ det ( ~A ) & = K ^ - n 1 det ( ~A ) det ( A ) & = K ^ - n aligned

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