A box for math with same height (and width) as some other math expression (especially for matrix elements/blocks)

Question

This is my MWE:

\documentclass[a4paper,12pt]{article}
\usepackage[T1]{fontenc}

\usepackage{mathtools}
\usepackage{physics}
\usepackage{easybmat}

\begin{document}
First attempt:  
    \begin{align*}
    &\left[\begin{BMAT}{c1c}{c1c}
        a& \begin{matrix} b_1& b_2 \end{matrix} \\
        \begin{matrix} c_1  \\ c_2 \end{matrix}&     D
    \end{BMAT}\right]
    \left[\begin{BMAT}{c1c}{c1c}
    a&  \mathmakebox[\widthof{$\begin{matrix} b_1& b_2 \end{matrix} $}]{\vb*b}\\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&    D
    \end{BMAT}\right]\\
    &\left[\begin{BMAT}{c1c}{c1c}
    a&  \mathmakebox[\widthof{$\begin{matrix} b_1& b_2 \end{matrix} $}]{\vb*b}\\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&    D
    \end{BMAT}\right]
    \end{align*}

Second attempt: 
        \begin{align*}
    &\left[\begin{BMAT}{c1c}{c1c}
    a& \begin{matrix} b_1& b_2 \end{matrix} \\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&     D
    \end{BMAT}\right]
    \left[\begin{BMAT}{c1c}{c1c}
    a& \begin{matrix}
    \mathmakebox[\widthof{$\begin{matrix} b_1& b_2 \end{matrix} $}]{\vb*b}
    \end{matrix}\\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&    D
    \end{BMAT}\right]\\
    &\left[\begin{BMAT}{c1c}{c1c}
    a& \begin{matrix}
    \mathmakebox[\widthof{$\begin{matrix} b_1& b_2 \end{matrix} $}]{\vb*b}
    \end{matrix}\\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&    D
    \end{BMAT}\right]
    \end{align*}
\end{document}

Here the mathtools package should be necessary for the command \mathmakebox; I'm using the easybmat package because it's a great tool for handling blocks in matrices, which is necessary for my purposes; the physics package here is used just for quick vector notation, but of course it's not necessary. One should get this result:

I often need to divide a matrix into several sectors, or merge several blocks into some bigger blocks, and so on… In doing this I often would like corresponding objects to have the very same visual dimensions.
In the MWE above, I tried to show how it is possible to make a "multi-column" matrix element of the same width of some consecutive elements in the same row with \mathmakebox and \widthof. [*]
In the "first attempt" it is shown that this trick works perfectly with horizontal spacing, but not with vertical spacing; in the "second attempt" a workaround for the vertical spacing is shown.
My questions are:

1. Is there any cleaner solutions than the one I used above (in the MWE)?
2. (fundamental) Is there a similar procedure to have a "multirow" matrix element of the same height of some consecutive elements within the same column?, in the MWE, just think of replacing the column (c₁,c₂) with a vector c, analogously to what has been done with (b₁,b₂) and b; I ask this especially because \heightof in \mathmakebox doesn't do the trick. [**]
3. (more general) Is there a way to make a box, intended to be filled with math, with the same dimensions (the height and width) of some other math expression?, eventually is there a way to use two different expressions, one for width and one for height?

[*] I have to add, here, that I usually avoid merging columns and/or rows when managing matrices; I find nesting matrices a simpler solution; of course, I may very well be wrong on this!, anyway this question may eventually make sense also for other purposes, unrelated to matrices.
[**] I may have a workaround also for this problem, by using boxes with null width in which putting phantom expressions; I refrained from posting it: it is so inelegant that, had I posted, I'd have been banned for ever.

Answer 1

You can avoid duplicate work by using a savebox.

\documentclass{article}
\usepackage{mathtools}
\usepackage{easybmat}

\newsavebox{\tempbox}% \sbox0 doesn't work

\begin{document}

\savebox\tempbox{$\begin{matrix} b_1 & b_2 \end{matrix}$}% must be outside align environment
\begin{align*}
    &\left[\begin{BMAT}{c1c}{c1c}
        a& \usebox\tempbox \\
        \begin{matrix} c_1  \\ c_2 \end{matrix}&     D
    \end{BMAT}\right]
    \left[\begin{BMAT}{c1c}{c1c}
    a&  \mathmakebox[\wd\tempbox]{\boldsymbol{b}}\\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&    D
    \end{BMAT}\right]\\
    &\left[\begin{BMAT}{c1c}{c1c}
    a&  \mathmakebox[\wd\tempbox]{\boldsymbol{b}}\\
    \begin{matrix} c_1  \\ c_2 \end{matrix}&    D
    \end{BMAT}\right]
    \end{align*}

\end{document}