Question

The determinant of all orthogonal matrices is 1 .

Short answer

Therefore, the given statement is false.

Step-by-step solution

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.

To check whether the given condition is true or false. 

The determinant of the orthogonal matrix is equal to -1 or -1.

Since,

$\det \left(A\right)=\det \left(A^T\right)$

and the determinant of product is the product of determinants. A when is an orthogonal matrix.

Therefore, the given statement is false.