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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]
