# the inverse of a matrix

• June 2nd 2009, 02:03 AM
xalk
the inverse of a matrix
Is the inverse of a matrix unique??

If yes how do we prove that ?
• June 2nd 2009, 03:32 AM
Random Variable
Assume that a nonsingular matrix has two inverse matrices and then show that the two matrices are equal to each other.
• June 2nd 2009, 11:26 AM
Gamma
The same proof to show inverses in a group are unique works.

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