On Matrix Elliptic Curves and Matrix Solutions of the Exponential Diophantine Equation (X²⁴-I₂₄)(Y²⁴-I₂₄)=Z²

We show that the structures of the matrix solutions of the matrix elliptic curves 2 3 6 EY X I : , α = +× ∈ α α  allow the construction of the matrix solutions of the equations 4 24 6 24 24 2 24 24 XY ZX IY I Z += − −= ,( )( ) . Mathematics Subject Classification(2010). 15B36, 11D61.