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Chapter 6: Q25E (page 309)

25. If the determinant of a square matrix is -1, then Amust be an orthogonal matrix.

Short Answer

Expert verified

The given statement is false.

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 the determinant of a square matrix is -1, thenmust be an orthogonal matrix or not.

For example,

A=12002

detA=2-12-0

detA=-1

A is not an orthogonal matrix, yet det A = - 1.

Therefore, the given condition is false.

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Most popular questions from this chapter

If all the diagonal entries of an n脳nmatrix Aare odd integers and all the other entries are even integers, thenA must be an invertible matrix.

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