Null space of $$$\left[\begin{array}{cc}-8 & 8\\8 & -8\end{array}\right]$$$
Your Input
Find the null space of $$$\left[\begin{array}{cc}-8 & 8\\8 & -8\end{array}\right]$$$.
Solution
The reduced row echelon form of the matrix is $$$\left[\begin{array}{cc}1 & -1\\0 & 0\end{array}\right]$$$ (for steps, see rref calculator).
To find the null space, solve the matrix equation $$$\left[\begin{array}{cc}1 & -1\\0 & 0\end{array}\right]\left[\begin{array}{c}x_{1}\\x_{2}\end{array}\right] = \left[\begin{array}{c}0\\0\end{array}\right].$$$
If we take $$$x_{2} = t$$$, then $$$x_{1} = t$$$.
Thus, $$$\mathbf{\vec{x}} = \left[\begin{array}{c}t\\t\end{array}\right] = \left[\begin{array}{c}1\\1\end{array}\right] t.$$$
This is the null space.
The nullity of a matrix is the dimension of the basis for the null space.
Thus, the nullity of the matrix is $$$1$$$.
Answer
The basis for the null space is $$$\left\{\left[\begin{array}{c}1\\1\end{array}\right]\right\}$$$A.
The nullity of the matrix is $$$1$$$A.