- A square matrix is said to be a LEFT INVERSE of if
- A square matrix is called a RIGHT INVERSE of if
- A matrix is said to be INVERTIBLE (or is said to have an INVERSE) if there exists a matrix such that

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- From the above lemma, we observe that if a matrix is invertible, then the inverse is unique.
- As the inverse of a matrix is unique, we denote it by That is,

By definition Hence, if we denote by then we get Thus, the definition, implies or equivalently

Proof of Part 2.

Verify that

Proof of Part 3.

We know
Taking transpose, we get

Hence, by definition height6pt width 6pt depth 0pt

A K Lal 2007-09-12