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Example of inserting a matrix
This shows how you can insert a matrix with square braces.
All things described in this wiki page and much more is described in the Math manual.
See the .lyx-file, it contains the example as well as instructions on how to do it.
Just download the file and open it with LyX
The example was produced using LyX 1.3.2 Qt.
The example doesn't contain any keyboard shortcuts for opening the math panel, or inserting a matrix.
Another way to create a matrix is with the \pmatrix, \matrix, \vmatrix commands, then extending the rows and columns with ctrl+enter and alt+m+c+c.