031 Review Part 2, Problem 9

If  $A$  is an  $n\times n$  matrix such that  $AA^{T}=I,$  what are the possible values of  ${\text{det }}A?$

Foundations:
Recall:
1.  ${\text{det }}(AB)=({\text{det }}A)({\text{det }}B)$
2.  ${\text{det }}I=n$
3.  ${\text{det }}A^{T}={\text{det }}A$

Solution:

Step 1:

Step 2:

Final Answer:

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