When $A^T = A^{-1}$ ?

Algebra Level pending

If $A$ is a square matrix and $A^T A= I ,$ the Identity matrix .

Which of the following is true?

$a. \$ Each column of $A$ has unit length and is perpendicular to every other column.

$b. \ A$ is an orthogonal matrix.

\text{Both} \ a \ \text{and} \ b

b

a

1 solution

Hana Wehbi
Mar 30, 2017

$a$ is the definition of $b$ . In Linear Algebra, an orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors.

When A T = A − 1 A^T = A^{-1} A T = A − 1 ?

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When $A^T = A^{-1}$ ?