Rank of a Matrix and Some Special Matrices

Yes, the rank of a matrix is zero if and only if the matrix is a null matrix, containing all zero entries.

A square matrix is invertible if and only if its rank equals the number of its columns (or rows), meaning it has full rank.

A matrix has full rank if its rank equals the maximum possible rank it can have, which is the lesser of its number of rows or columns. This condition indicates that the matrix's column vectors are linearly independent.