How on Mathematica would you determine if matrix has an inverse?

Questions
,
1

Here is the matrix

a={{1,7,5,0},{5,8,6,9},{2,1,6,4},{8,1,2,4}}
2

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

3

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 *)