You could use array nested in array, but in this case I believe aligned is better:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\left[
\begin{aligned}
o_1 & \mapsto
\left[
\begin{aligned}
o_1 & \mapsto 1 \\
o_2 & \mapsto 0 \\
o_3 & \mapsto 0
\end{aligned}
\right]
\\
o_2 & \mapsto
\left[
\begin{aligned}
o_1 & \mapsto 1 \\
o_2 & \mapsto 1 \\
o_3 & \mapsto 0
\end{aligned}
\right]
\\
o_3 & \mapsto
\left[
\begin{aligned}
o_1 & \mapsto 0 \\
o_2 & \mapsto 0 \\
o_3 & \mapsto 1
\end{aligned}
\right]
\end{aligned}
\right]
\end{equation*}
\end{document}

Without overshooting:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\begin{bmatrix}
\begin{aligned}
o_1 & \mapsto
\begin{bmatrix}
\begin{aligned}
o_1 & \mapsto 1 \\
o_2 & \mapsto 0 \\
o_3 & \mapsto 0
\end{aligned}
\end{bmatrix}
\\
o_2 & \mapsto
\begin{bmatrix}
\begin{aligned}
o_1 & \mapsto 1 \\
o_2 & \mapsto 1 \\
o_3 & \mapsto 0
\end{aligned}
\end{bmatrix}
\\
o_3 & \mapsto
\begin{bmatrix}
\begin{aligned}
o_1 & \mapsto 0 \\
o_2 & \mapsto 0 \\
o_3 & \mapsto 1
\end{aligned}
\end{bmatrix}
\end{aligned}
\end{bmatrix}
\end{equation*}
\end{document}
