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If a is an Invertible Matrix, Then Which of the Following is Not True ? - Mathematics

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प्रश्न

If A is an invertible matrix, then which of the following is not true ?

पर्याय

  • \[\left( A^2 \right)^{- 1} = \left( A^{- 1} \right)^2\]

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

  • \[\left( A^T \right)^{- 1} = \left( A^{- 1} \right)^T\]

  • \[\left| A \right| \neq 0\]

MCQ
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उत्तर

\[\left( A^2 \right)^{- 1} = \left( A^{- 1} \right)^2\]

We have, \[\left| A^{- 1} \right| = \left| A \right|^{- 1}\], \[\left( A^T \right)^{- 1} = \left( A^{- 1} \right)^T\] and \[\left| A \right| \neq 0\] all are the properties of the inverse of a matrix A.

 

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पाठ 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [पृष्ठ ३७]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 1 | पृष्ठ ३७

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