Proof that inverse of a matrix is unique _If B and C are both inverses of the matrix A,then B=C_. Can't i prove it in following way ? Proof: `AB=BA=I` and `AC=CA=I`,then `BA=CA=I` By postmultiplication $\Rightar...--prophetes.ai

Proof that inverse of a matrix is unique _If B and C are both inverses of the matrix A,then B=C_. Can't i prove it in following way ? Proof: `AB=BA=I` and `AC=CA=I`,then `BA=CA=I` By postmultiplication $\Rightarrow (BA)(A^{-1})=(CA)(A^{-1})=(I)(A^{-1})\Rightarrow B=C=A^{-1}$, or by premultiplication $AB=AC=I\Rightarrow (A^{-1})(AB)=(A^{-1})(AC)=(A^{-1})(I)\Rightarrow B=C=A^{-1}$.

There is much much simpler.

$B=BI=B(AC)=(BA)C=IC=C$