Question: Determine whether the following set is a real vector space (and select what fails if it is not). The set of all upper triangular square

Determine whether the following set is a real vector space (and select what fails if it is not).

The set of all upper triangular square matrices

Closure under Addition

Closure under Scalar Multiplication

Commutativity of Addition

Associativity of Addition

Existence of Zero Vector

Existence of Additive Inverses

Multiplicative Identity

Associativity of Scalar Multiplication

Distributivity over Vector Addition

Distributivity over Scalar Addition

The set is a real vector space.

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