  We investigate the notions of amenability and its related homological notions
for a class of $I\times I$-upper triangular matrix algebra, say $UP(I,A)$,
where $A$ is a Banach algebra equipped with a non-zero 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 the notions
of pseudo-amenability and approximate biprojectivity of $UP(I,A)$.
