Question

NOTE:----------->
This is only a tutorial.
The inverse of a square matrix, if it exists, is unique. Prove this theorem.

Answer 1

Proof:----------->for this above stated theorem

Answer 2

Proof:--is as follows..

Answer 3

Let [A]=aij be a square matrix.
If possible, let B & C be 2 inverses of this matrix.then we can say that

Answer 4

AB=BA=I (since B is inverse of A).
AC=CA=I (since C is inverse of A).
Here, I=Unit/identity matrix.

Answer 5

Now, we can say that
B=BI.
=>B(AC)=BA(C)=I(C)=C
Thus, B=C.

Answer 6

Thus we can say that any square matrix has a unique inverse for itself.
\[H.P.\]