Inverse of a Matrix

Inverse of a Matrix

Suppose A is a given matrix. If there exists a matrix B such that, AB = I = BI then A is said to be an invertible matrix and B is called as inverse of A and is denoted by

A Inverse

Note:- If a matrix A posses an inverse then A is a square matrix and inverse of A is unique.
Proof:-
Since A is invertible there exists a matrix B such that AB = I = BI.
Since AB = BA, A is necessarily a square matrix.
If possible suppose C is also inverse of A which implies AC = I = CA
B = B. I = B (AC) = (BA)C = I.C = C

Therefore If any matrix posses an inverse then it has to be unique.

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