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If D is the Determinant of a Square Matrix a of Order N, Then the Determinant of Its Adjoint is - Mathematics

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Question

If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is _____________ .

Options

  • dn

  • dn−1

  • dn+1

  • d

MCQ
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Solution

dn−1

We know,

\[\left| adjA \right| = \left| A \right|^{n - 1}\]

\[\Rightarrow \left| adjA \right| = d^{n - 1}\]

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Chapter 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [Page 38]

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RD Sharma Mathematics [English] Class 12
Chapter 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 18 | Page 38

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