If A is a singular matrix, then adj A is ______. - Mathematics

Question

If A is a singular matrix, then adj A is ______.

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non-singular
singular
symmetric
not defined

MCQ

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Solution

If A is a singular matrix, then adj A is singular.

$A is singular, so | A | = 0$ .

By definition, we have

A $a d j (A) = O$

$\Rightarrow | A a d j (A) | = | O |$

$\Rightarrow | A | | a d j (A) | = 0$

$\Rightarrow | a d j (A) | = 0$

$Hence, a d j (A) is singular$ .

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Inverse of Matrix - Inverse of a Square Matrix by the Adjoint Method

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Chapter 7: Adjoint and Inverse of a Matrix - Exercise 7.4 [Page 37]

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Chapter 7 Adjoint and Inverse of a Matrix
Exercise 7.4 | Q 5 | Page 37

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