MatrixRank
MatrixRank[m] gives the rank of the matrix m (the number of linearly independent rows or columns).
Examples
Compute matrix rank:
MatrixRank[{{1, 2}, {3, 4}}]
(* 2 *)
(* Singular matrix has lower rank *)
MatrixRank[{{1, 2, 3}, {2, 4, 6}, {1, 1, 1}}]
(* 2 *)
(* Identity matrix *)
MatrixRank[IdentityMatrix[5]]
(* 5 *)Please visit the official Wolfram Language Reference for more details.