Answer the following questions about square matrices and of the same order .

MATHEMATICS · Multi-part · CBSE · Mathematics · Matrices · Matrices

Problem

Answer the following questions about square matrices

A

and

B

of the same order

n

. (i) If

AB=I_n

, explain why both

A

and

B

must be non-singular matrices. (ii) Under the same hypothesis

AB=I_n

, is it always true that

BA=I_n

? Give a reasoned justification for your answer.