RANK OF A MATRIX
A number r is said to be the rank of an m x n matrix A if
(i) every square submatrix of order ( r + 1) or more is singular, and
(ii) there exists atleast one square submatrix of order r which is non-singular.
Thus, the rank of a matrix is the other of the highest order non-singular square submatrix.
NOTE :
(i) The rank of null matrix is zero and the rank of every non-null matrix is greater than or equal to 1.
(ii) Rank of identity matrix of order n is n.
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