If A and B are 3 × 3 real matrices such that rank(AB) = 1, then rank(BA) cannot be

Are there two 3 by 3 matrices A and B, both of rank 2,such that AB is the zero matrix? Explain your answer

Find the value of b such that the rank of the matrix A is 3.A =[1 1 −1 04 4 −3 1𝑏 2 2 29 9 𝑏 3

Let A and B are two 3×3 non-zero real matrices and AB=0, then which of the following option is correct ?

Consider the 4\times 3 matrix \boldsymbol{A} defined by A=[100 220 -11a 01b] where a and b are real numbers. What is the smallest value of the rank of \boldsymbol{A} that can be achieved by choosing a and b?

Give three equivalent definitions of the rank of a matrix. Write down a 3 × 3 matrix of rank 1, anduse one of your definitions to prove that your example is correct.