The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix.

If we consider a square matrix, the columns (rows) are linearly independent only if the matrix is nonsingular.

In other words, the rank of any nonsingular matrix of order m is m. Rank of a matrix A is denoted by ρ(A).

Symbol: The Rank of a matrix is represented by ρ( A ) or Rank(A).If A is of order n×n and |A| ≠ 0, then the rank of A = n. If A is of order n×n and |A| = 0, then the rank of A will be less than n.