Short Answer

If a square matrix $A$ is invertible, then its classical adjoint $adj (A)$ is invertible as well.

Therefore, the $a d j (A)$ is invertible, $d e t a d j A \neq 0$ So, the given statement is true.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Orthogonal Matrix Definition

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

Step 2: To check whether the given condition is true or false

If a square matrix $A$ is invertible, then we have

$A^{- 1} = \frac{1}{d e t A} a d j A$

Therefore,

$0 \neq d e t A^{- 1} = d e t (\frac{1}{d e t A} a d j A)$

$d e t a d j A \neq 0$

Therefore, the $a d j (A)$ is invertible, $d e t a d j A \neq 0$ So, the given statement is true.

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Linear Algebra With Applications

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Short Answer

If a square matrix $A$ is invertible, then its classical adjoint $adj (A)$ is invertible as well.

Step by Step Solution

Step 1: Orthogonal Matrix Definition

Step 2: To check whether the given condition is true or false

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Linear Algebra With Applications

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Short Answer

If a square matrix A is invertible, then its classical adjoint adj(A) is invertible as well.

Step by Step Solution

Step 1: Orthogonal Matrix Definition

Step 2: To check whether the given condition is true or false

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If a square matrix $A$ is invertible, then its classical adjoint $adj (A)$ is invertible as well.