Let $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_2$ be a bent function (i.e. the Walsh transform of $f$ is $\mathcal{W}_{f}(a)=\sum_{x \in \mathbb{Z}_2^n}(-1)^{f(x)+a\cdot x}=\pm2^{n/2}$ for all $a \in \mathbb{Z}_2^n$). Prove that $g(x)=f(Ax+b)$ is also a bent function where $A$ is an invertible $n\times n $ matrix over $\mathbb{Z}_2^n$ and $b \in \mathbb{Z}_2^n$.
Since $A$ is invertible we can write the Walsh transform of $g$ as $$\mathcal{W}_{g}(a)=(-1)^d\sum_{y \in \mathbb{Z}_2^n}(-1)^{f(y)+c\cdot (By)}$$ for some $B$ and $c, d$ associated to $A$ and $a$. I'm not sure how to proceed?