Help with this Transpose and Identity Problem please

Let A be a square matrix such that AA^T= I. Show that lAl = /- 1

Start with AA^t = I.

Take the determinant of both sides:
|AA^t| = |I|
==> |A| |A^t| = |I|, since |AB| = |A| |B|
==> |A| |A| = 1, since |A^t| = |A|, and |I| = 1
==> |A|^2 = 1.

Take square roots of both sides:
|A| = ±1.

I hope this helps!