6 triple backslashes !!

I just cannot get this thing to make the 2 by 2 matrices of letters I want. Help!Wait, fixed it myself. There is a thread in Meta about Latex/jsMath inconsistencies, one known problem is backslash being interpreted as an escape. So where I intended double backslash I just put three backslashes and that works for now. If it fails later I will switch to four or five backslashes.

Given a square matrix $M \in SO_n$ decomposed as illustrated (well, pretend ) with square blocks $A,D$ and rectangular blocks $B,C,$

$$M = \left( \begin{array}{cc} A & B \\ C & D \end{array} \right) ,$$

then $\det A = \det D.$

What this says is that, in Riemannian geometry with an orientable manifold, the Hodge star operator is an isometry, a fact that has relevance for Poincare duality.

http://en.wikipedia.org/wiki/Hodge_duality

http://en.wikipedia.org/wiki/Poincar%C3%A9_duality

But the proof is a single line, (I intend a multiplication of square matrices):

$$\left( \begin{array}{cc} A & B \\ 0 & I \end{array} \right) \left( \begin{array}{cc} A^t & C^t \\ B^t & D^t \end{array} \right) = \left( \begin{array}{cc} I & 0 \\ B^t & D^t \end{array} \right).$$

5 added 2 characters in body

I just cannot get this thing to make the 2 by 2 matrices of letters I want. Help!

Given a square matrix $M \in SO_n$ decomposed as illustrated (well, pretend ) with square blocks $A,D$ and rectangular blocks $B,C,$

$M$M = \left( \begin{array}{cc} A & B \
C & D \end{array} \right) ,$$then \det A = \det D. What this says is that, in Riemannian geometry with an orientable manifold, the Hodge star operator is an isometry, a fact that has relevance for Poincare duality. http://en.wikipedia.org/wiki/Hodge_duality http://en.wikipedia.org/wiki/Poincar%C3%A9_duality But the proof is a single line, (I intend a multiplication of square matrices):$$ \left( \begin{array}{cc} A & B \ 0 & I \end{array} \right) \left( \begin{array}{cc} A^t & C^t \ B^t & D^t \end{array} \right) = \left( \begin{array}{cc} I & 0 \ B^t & D^t \end{array} \right). $$4 added 76 characters in body I just cannot get this thing to make the 2 by 2 matrices of letters I want. Help! Given a square matrix M \in SO_n decomposed as illustrated (well, pretend these are genuine 2 by 2 matrices) with square blocks A,D and rectangular blocks B,C, M = \left( \begin{array}{cc} A & B \ C & D \end{array} \right) , then \det A = \det D. What this says is that, in Riemannian geometry with an orientable manifold, the Hodge star operator is an isometry, a fact that has relevance for Poincare duality. http://en.wikipedia.org/wiki/Hodge_duality http://en.wikipedia.org/wiki/Poincar%C3%A9_duality But the proof is a single line, (I intend a multiplication of 2 by 2 square matrices):$$ \pmatrix{ left( \begin{array}{cc} A & B \ 0 & I } \; end{array} \pmatrix{ right) \left( \begin{array}{cc} A^t & C^t \ B^t & D^t } \; end{array} \; right) = \; left( \;\pmatrix{ begin{array}{cc} I & 0 \ B^t & D^t }. \end{array} \right). 

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