Question

The entries of an orthogonal matrix are all less than or equal to 1.

Short answer

True

Step-by-step solution

Step by step solution Step 1: Definition of an orthogonal matrix

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.

Determine whether the statement is true or false

For example,

Suppose A is a square matrix with real elements and of n x norder and $A^T$is the transpose of A. Then according to the definition, if$A^T=A^{-1}$ is satisfied, then,

$A{A}^T=I$

Since, the columns vectors are the unit vectors.

Hence, the statement is true.