Respuesta :

lublana

Answer with Step-by-step explanation:

Let A is non-singular

[tex]\mid A\mid\neq 0[/tex]

We have to prove that [tex]A^{-1}[/tex] is unique.

Suppose B and C are inverse of A such that

[tex]BA=I[/tex] and AC=I

By using property [tex]AA^{-1}=A^{-1}A=I[/tex]

[tex]C=C[/tex]

[tex](BA)C=B(AC)[/tex]

[tex]I\cdot C=B\cdot I[/tex]

[tex]C=B[/tex]

Hence, the inverse of A is unique.