Definition: Invertible and Inverse Matrix

Let \(A\in M_{n\times n}(F)\) be a square matrix. If there exists another square matrix \(B\in M_{n\times n}(F)\) which, when multiplied with \(A\), results in the identity matrix:

\[AB=BA=I,\]

then we call \(A\) an invertible matrix and \(B=A^{-1}\) its inverse matrix.

Examples: 1


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References

Bibliography

  1. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994