Answer:
C) II only
Step-by-step explanation:
Given the 2×2 matrix A = [1 1, 0 1]
The only statement true there is (II) only i.e the matrix is not diagonalizable but invertible. A matrix is invertible if the product of the matrix and its inverse is equal to an identity matrix
The rank of the matrix is not 1 but 2 because rank of a matrix is the number of non zero rows of a matrix and the number of non zero rows of this matrix is 2 thereby making I incorrect.
Also note that the sum of nullity and rank is equal to the number of columns of the given matrix
Nullity + rank = number of columns
Nullity = number of columns - rank
Nullity = 2-2 = 0
The nullity is therefore 0 not 1 making option III also false
