Here is the matrix
a={{1,7,5,0},{5,8,6,9},{2,1,6,4},{8,1,2,4}}
Could check that #rows==#cols==rank.
a = {{1, 7, 5, 0}, {5, 8, 6, 9}, {2, 1, 6, 4}, {8, 1, 2, 4}}; MatrixQ[a] && MatrixRank[a] == Length[a] == Length[a[[1]]] (* Out[210]= True *)
A matrix is invertible if and only if its determinant is non-equal zero. Therefore,
Det[a]
will give you the result. If you want a language output:
If[Det[a] != 0, "The matrix is invertible.", "The matrix is not invertible."]
Of course you can also just calculate the Inverse.
Inverse[a]
If there is no inverse Mathematica will tell you that the matrix is singular.
Best wishes,
Marco
