Let AAA be a 2×22 \times 22×2 matrix with eigenvalues λ1=2,λ2=3\lambda_1 = 2, \lambda_2 = 3λ1=2,λ2=3. If A=PDP−1A = PDP^{-1}A=PDP−1 with D=(2003)D = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}D=(2003), what is det(ATA)\det(A^T A)det(ATA)?
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