Let A and B be non-singular matrices of the same order such that A B=A and B A=B . Which of the following statements is/are correct? 1. A^2=A 2. A B^2=A^2 B Select the correct answer using the code given below :

Step-by-step solution

aligned & Given that |A| 0,|B| 0 & A B=A A⁻¹ A B=A⁻¹ A B=I & and B A=B B⁻¹ B A=B⁻¹ B & A=I & A^2=I^2=I=A aligned So, statement 1 is correct aligned & Now, aligned & A B^2=I^3=I & A^2 B=I^3=I & A B^2=A^2 B aligned aligned So, statement 2 is correct