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Adjoint of a Matrix

If A is an ...

Question

If $A$ is an invertible matrix. then which of the followings are true:

A \neq 0

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Adj.

A \neq 0

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| A | \neq 0

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A^{- 1} = | A | A d j . A .

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Solution

The correct options are
A Adj. $A \neq 0$
B $A \neq 0$
D $| A | \neq 0$
A is invertible matrix
$\Rightarrow A^{- 1}$ exists
$\Rightarrow | A | \neq 0$
$A d j A \neq 0$
$A \neq 0$
Option A, B, C are correct

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