You got the syntax right, but if arr_ is an immediate member of the class (and it probably is), then you simply can't return a non-cost reference to this member. Inside the above arr method, member arr_ is seen as having const Chips[6][7] type. You can't use this type to initialize a reference of Chops (&)[6][7] type since it would break const-correctness. In order for the above to compile you'd need a const on the returned reference as well
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const Chips (&arr() const)[6][7] { return arr_; }
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But in any case, you'll be much better off with a typedef
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typedef Chips Chips67[6][7];
const Chips67 &arr() const { return arr_; }
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