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Block matrix with array, NiceMatrix or tabularray

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About this code I'd like that only between $a_{11}$ and $a_{12}$ there isn't the vertical line. How can I do?I'd desire to have three solutions, one with normal \begin-\end array, another with pNiceMatrix and the last with tabularray.Furthermore is there a way to color the block matrix rectangle of vertices $a_{22},b_2,a_{n2},b_n$?Thank you so much

\documentclass{book}\usepackage{mathtools}\usepackage{nicematrix}\usepackage{stix}\usepackage{tabularray}\usepackage{xcolor,color}\newcommand{\Tonde}[1]{\left(#1\right)}\begin{document}\begin{equation}\Tonde{\begin{array}{c|ccc|c}a_{11}&a_{12}&\cdots&a_{1n}&b_1\\\cline{2-5}a_{21}&a_{22}&\cdots&a_{2n}&b_2\\\vdots&\vdots&\ddots&\vdots&\vdots\\a_{n1}&a_{n2}&\cdots&a_{nn}&b_n\end{array}}\end{equation}   \end{document}

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