If B is invertible, prove that AB^(-1)=B^(-1) A if and only if AB=BA.

kasibug1v

kasibug1v

Answered question

2022-10-07

Let A and B be arbitrary n × n matrices. If B is invertible, prove that A B 1 = B 1 A if and only if AB=BA

Answer & Explanation

Marcel Mccullough

Marcel Mccullough

Beginner2022-10-08Added 11 answers

To prove , A B 1 = B 1 A iff A B = B A
A B 1 = B 1 A
B A B 1 B = B B 1 A B
B A I = I A B
B A = A B
A B = B A

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