There is no set syntax for Wolfram|Alpha. To see examples of how to write a matrix, see the Wolfram|Alpha example pages:
https://www.wolframalpha.com/examples/Matrices.html
For example, you can ask for the determinant of a matrix with:
"determinant of {{3,0,0,4},{2,1,0,1},{5,3,4,0},{6,6,7,2}}"
If you want to use a set syntax and work with larger matrices, I suggest using Mathematica online. http://www.wolfram.com/mathematica/online/