If A is a square matrix satisfying A T A = I, write the value of |A|.

Question

Philoid · Accepted Answer

Since A^TA=I

Taking determinant both sides

|A^TA|=|I|

Using |AB|=|A||B|,

|A^T|=|A| and |I|=1, we get

|A||A|=1

(|A|)²=1

Hence, |A|=±1