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Does there exists any triple $(A,B,C)$ of $n\times n$ matrices with integer entries which satisfies $A^k+B^k=C^k$ for at least one $k\geq3$? Here $n,k$ are given to us, that is, we can choose them according to our convenience.

Does there exists any triple $(A,B,C)$ of $n\times n$ $n\geq3$ matrices with integer entries which satisfies $A^k+B^k=C^k$ for at least one $k\geq3$? Here $n,k$ are given to us, that is, we can choose them according to our convenience.

Does there exists any triple $(A,B,C)$ of $n\times n$ $n\geq3$ ($n\geq3$) matrices with integer entries which satisfies $A^k+B^k=C^k$ for at least one $k\geq3$? Here $n,k$ are given to us, that is, we can choose them according to our convenience.

Does there exists any triple $(A,B,C)$ of $n\times n$ ($n\geq3$) matrices with integer entries which satisfies $A^k+B^k=C^k$ for at least one $k\geq3$? Here $n,k$ are given to us, that is, we can choose them according to our convenience.

Does there exists any triple $(A,B,C)$ of $n\times n$ ($n\geq3$) matrices with integer entries which satisfies $A^k+B^k=C^k$ for at least one $k\geq3$? Here $n,k$ are given to us, that is, we can choose them according to our convenience.