We investigate the amenability and its related homological notions for a class of I ×I-upper triangular matrix algebra, say UP(I, A), where A is a Banach algebra equipped with a nonzero character. We show that UP(I, A) is pseudo-contractible (amenable) if and only if I is singleton and A is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of UP(I, A).
