Answer with Step-by-step explanation:
Suppose that a matrix has two inverses B and C
It is given that AB=I and AC=I
We have to prove that Inverse of matrix is unique
It means B=C
We know that
B=BI where I is identity matrix of any order in which number of rows is equal to number of columns of matrix B.
B=B(AC)
B=(BA)C
Using associative property of matrix
A (BC)=(AB)C
B=IC
Using BA=I
We know that C=IC
Therefore, B=C
Hence, Matrix A has unique inverse .