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Answer:

  det(A·A^T) = (a² -1)²

Step-by-step explanation:

The determinant of A is ...

  det(A) = a·a -x·y = a² -1

The determinant of the transpose is the same, and the determinant of a matrix product is the product of the determinants.

  [tex]|A\cdot A^T|=|A|^2=\boxed{(a^2-1)^2=a^4-2a^2+1}[/tex]

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