Ygtjki

I wish to write the following block matrix in LaTex.

I have been trying a bunch of stuff, but none of it seems to work. In particular, I tried the following:

beginbmatrix
0 & -1& & & & & 0 & & & &\
1 & 0 & & & & & & & & &\
 & & cdot & & & & & & & &\
 & & & cdot & & & & & & &\
 & & & & cdot & & & & & &\
 & & & & & 0 & 1 & & & &\
 & & & & &-1 & 0 & & & &\
 & & & & & & & cdot & & &\
 & & & & & & & & cdot & & \ 
 & & & & & & & & & cdot & \
0 & & & & & & & & & & 0\ 
endbmatrix

But this is pretty ugly and so any suggestions will be much appreciated.

Perhaps

$left(beginarraycccccc
left[beginarraycc
0 & 1\
-1 & 0
endarrayright] & & & & & 0\
 & ddots\
 & & left[beginarraycc
0 & 1\
-1 & 0
endarrayright]\
 & & & 0\
 & & & & ddots\
0 & & & & & 0
endarrayright)$ 

Here there is my proposal as the original picture using bmatx command that replace a boxed matrix.

documentclassarticle
usepackagemathtools
newcommandbmatxboxedbeginmatrix 0& 1 \ -1& 0endmatrix

begindocument
[
beginpmatrix
, bmatx& & & & & & & 0 \ 
 & ddots& & & & \ 
 & & bmatx & & & & \ 
 & & & ddots& & &\ 
 & & & & 0 & &\ 
 & & & & & & ddots\ 
0 & & & & & & & 0 
endpmatrix
]

enddocument

The best code is provided thanks to the precious comment of @Bernard.

Just for the fun of it! :-)

documentclassarticle
usepackageamsmath,array

begindocument

[
beginpmatrix
newcommandlr[1]multicolumn1#1
newcommandrr[1]multicolumn1c#1
;
beginarray@*10c@
cline1-2
lr0 & rr1 &&&&&&&& raisebox-1em[0pt][0pt]$0$\
lr-1 & rr0 \
cline1-2
&& ddots \
cline4-5
&&& lr0 & rr1 \
&&& lr-1 & rr0 \
cline4-5
&&&&& 0 \[-1ex]
&&&&&& ddots \
&&&&&&& 0 \[-1ex]
&&&&&&&& ddots \
multicolumn2c0 &&&&&&&& 0
endarray
;;
endpmatrix
]

enddocument

Here's another solution. It uses a pmatrix environment for the overall matrix and a custom macro called blockmat for the 2x2 inner matrices.

documentclassarticle
usepackagearray,amsmath
newcommandblockmat%
 beginarray
 hline 0 & 1^mathstrut \ -1 & 0 \ hline
 endarray
begindocument
[
beginpmatrix
blockmat & & & & & 0 \
 & ddots & & & & \
 & & blockmat & & & \
 & & & 0 & & \
 & & & & ddots & \
0 & & & & & 0 \ 
endpmatrix
]
enddocument