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.
