If-A-is-an-invertible-matrix-then-det-A-1-is-equal-to-

Question Number 107331 by saorey0202 last updated on 10/Aug/20

If A is an invertible matrix, then \det (A^{- 1})

is equal to

Answered by udaythool last updated on 10/Aug/20

{A A}^{- 1} = I

\Rightarrow∣ {A A}^{- 1} ∣=∣ A ∣ \cdot ∣ A^{- 1} ∣=∣ I ∣= 1

\Rightarrow∣ A^{- 1} ∣= \frac{1}{∣ A ∣}