it‘s not always right.
Because Rank(A) <= min(row,column) is the right condition.
So, we can’t presume that rank will always be equals to min(row, column).
here it can be anything less than or equal to 4. so, we need to consider other properties and take up to the right answer. Here, by considering nullity to get the rank of the matrix in the given question.
here, Nullity is 1, and by considering the dimension theorem
rank(P) + nullity(P) = number of dimension(P)
rank(P) = number of dimension(P) – nullity(P)
rank(P) = 5 – 1 = 4.