Applied Mathematics · Ch 2 — Algebra

Finding Inverse Matrix by Inverse of Coefficient Matrix Method

2.7.2

Finding Inverse Matrix by Inverse of Coefficient Matrix Method

Recall that for any square matrix $A$ of order $n$ , the adjoint satisfies $A(\text{adj}\,A) = (\text{adj}\,A)A = |A|\,I$ . Dividing through by $|A|$ , whenever that's possible, immediately gives a ready-made formula for the inverse:

A^{-1} = \dfrac{1}{|A|}\,\text{adj}\,A

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