Q21 of 256 Page 7

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

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

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