Question

Prove that if BA=I then BA=AB.

Answer 1

Answer with Step-by-step explanation:

Since we have given that

$BA=I$

As we know that

AA⁻¹ = I (A is invertible matrix)

Multiplying A⁻¹ on the both the sides:

$BAA^{-1}=IA^{-1}\\\\B=A^{-1}$

Using the above result, we get that

$BA=I=AA^{-1}\\\\BA=AB$

Therefore, BA = AB

Hence, proved.