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Let S be the commutative and idempotent semiring with additive identity 0 and multiplicative identity 1 . The tropical semiring T and the Boolean semiring B are common important examples of such semirings. Let U T n (S) be the semigroup of all n × n upper triangular matrices over S , both U T n ± (S) and U T n + (S) be subsemigroups of U T n (S) with 0 and/or 1 on the main diagonal, and 1 on the main diagonal respectively. It is known that U T 2 (T) is non-finitely based and U T 2 ± (S) is finitely based. Combining these results, the finite basis problems for U T n (T) and U T n ± (S) with n = 2 , 3 both as semigroups and involution semigroups under the skew transposition are solved. It is well known that the semigroups U T n + (S) and U T n + (B) are equationally equivalent. In this paper, we show that the involution semigroups U T n + (S) and U T n + (B) under the skew transposition are not equationally equivalent. Nevertheless, the finite basis problems for involution semigroups U T n + (S) and U T n + (B) share the same solution, that is, the involution semigroup U T n + (S) is finitely based if and only if n = 2 . [ABSTRACT FROM AUTHOR]