Consider the following statements in respect of square matrices A and B of same order: 1. If A B is a null matrix, then at last one of A and B is a null matrix. 2. If A B is an identity matrix, then B A=A B . Which of the above statements is/are correct?

Step-by-step solution

Let A= [ array ll 1 & 1 1 & 1 array ] and B= [ array cc 1 & -1 -1 & 1 array ]A B= [ array ll 1 & 1 1 & 1 array ] [ array cc 1 & -1 -1 & 1 array ]= [ array ll 0 & 0 0 & 0 array ] But A 0 and B 0 So, statement I is not correct A B= I B=A⁻¹ B A=I So, statement 2 is correct.