Answer
the set of vectors is linearly independent set of vectors.
Work Step by Step
Consider the combination
$$a \left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right]+b\left[\begin{array}{cc}{0} & {1} \\ {0} & {0}\end{array}\right]+c\left[\begin{array}{ll}{0} & {0} \\ {0} & {0}\end{array}\right]=0, \quad a,b,c\in R.$$
Which yields the following system of equations
\begin{align*}
a&=0\\
b&=0.
\end{align*}
Then the set of vectors is linearly independent set of vectors.