If-A-B-are-two-square-matrices-such-that-AB-A-and-BA-B-then-

Question Number 98369 by nesreen last updated on 13/Jun/20

If A, B are two square matrices such

that A B = A and B A = B, then

Answered by bobhans last updated on 13/Jun/20

A^{- 1} AB = A^{- 1} A \Rightarrow B = I

B^{- 1} BA = B^{- 1} B \Rightarrow A = I

then A = B = I

Answered by Rio Michael last updated on 13/Jun/20

Also A B = A and B A = B

\Rightarrow A (B A) = A

\Rightarrow (A B) A = A

\Rightarrow (A) (A) = A

\Rightarrow A^{2} = A similarly, B^{2} = B