linear algebra - Determine whether the set $H$ of all matrices form a subspace of $M_{2 times 2}$

Determine if the set $Z$ of all matricies form
$\left[ \begin{array}{cc} a & b \\ 0 & d \end{array} \right]$
is a subspace of $M_{2 \times 2}$ (the set of all $2 \times 2$ matrices).

% This is something I came up with. Can someone look at it and let me know any useful corrections/suggestions to the question please.

Answer:

Without specification as to the nature of $a,b$ and $d$, it is assumed that $a,b,d \in \mathbb{R}$

Hence, $H$ is determined to be a subspace of $M_{2 \times 2}$ because it is closed under scalar addition and scalar multiplication and contains the zero vector when $a=b=d=0$.