the inverse of a matrix

**xalk** · June 2nd 2009, 01:03 AM

Is the inverse of a matrix unique??

If yes how do we prove that ?

**Random Variable** · June 2nd 2009, 02:32 AM

Assume that a nonsingular matrix has two inverse matrices and then show that the two matrices are equal to each other.

**Gamma** · June 2nd 2009, 10:26 AM

The same proof to show inverses in a group are unique works.

Let $A_1^{-1}$ and $A_2^{-1}$ be inverses of A.
$A_1^{-1}=A_1^{-1}I_n=A_1^{-1}(AA_2^{-1})=(A_1^{-1}A)A_2^{-1}=I_nA_2^{-1}=A_2^{-1}$

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