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Chapter 5: Q13E (page 263)

TRUE OR FALSE?If matrix A is orthogonal, then the matrixAT must be orthogonal as well.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Recollect the properties of the orthogonal a matrix.

According to the properties of a orthogonal matrix, if an脳nmatrix Ais an orthogonal matrix, thenA-1=AT.

Also, if Ais an orthogonal matrix, thenA-1is also orthogonal.

02

Check whether the given statement is a true or false.

The given statement is if the matrix A is orthogonal, then the matrixAT must be orthogonal as well.

Here,A is orthogonal. This means,A-1 is also orthogonal, andA-1=AT

This means,AT is also an orthogonal matrix.

It is clear that, the given statement is true, by the properties of orthogonal matrices.

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