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Chapter 6: Q39E (page 309)

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

Short Answer

Expert verified

Therefore, the adjAis invertible, detadjA鈮�0 So, the given statement is true.

Step by step solution

01

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.

02

To check whether the given condition is true or false

If a square matrix Ais invertible, then we have

A-1=1detAadjA

Therefore,

0鈮�detA-1=det1detAadjA

detadjA鈮�0

Therefore, the adjAis invertible, detadjA鈮�0 So, the given statement is true.

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Most popular questions from this chapter

Find the determinants of the linear transformations in Exercises 17 through 28.

22.T(f(t))=f(-t)fromPntoPn

Find the determinants of the linear transformations in Exercises 17 through 28.

18.T(f)=2f+3f'fromP2toP2

There exist real invertible 3脳3 matrices A andSsuch thatS-1AS=2A .

The determinant of all orthogonal matrices is 1 .

There exists a 4脳4 matrix whose entries are all 1or -1 , and such thatdetA=16.
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