The determinant of a orthogonal matrix is :

• A: ±1
• B: 2
• C: 0
• D: ±2

The determinant of an orthogonal matrix has specific properties that are important in linear algebra.

Key Characteristics of Orthogonal Matrices

An orthogonal matrix is defined by the property that its transpose is equal to its inverse. This means that when you multiply an orthogonal matrix by its transpose, you get the identity matrix.

Determinant Values

For orthogonal matrices, the determinant can only take on certain values. Specifically, the determinant can be either +1 or -1. This indicates that orthogonal matrices preserve lengths and angles, making them significant in various applications, including rotations and reflections.

Correct Answer

• A: ±1 is the correct choice.
• B: 2 is incorrect.
• C: 0 is incorrect.
• D: ±2 is incorrect.

In summary, the determinant of an orthogonal matrix is always ±1.