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## Computation of determinant

Linear Algebra
Riemann
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### Computation of determinant

Let $A, B \in \mathcal{M}_{2 \times 2}$ be matrices with integer entries such that $AB = BA$ , $\det \left( A + B \right) =2$ and $\det \left( A^3 + B^3 \right) = 2^3$. Evaluate the determinant

$$\mathcal{D} = \det \left( A^2 + B^2 \right)$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$