The determinant of an inverse

ProofProperties of the determinant

Let $A$ be an invertible $n \times n$ matrix. Prove that $\det A \neq 0$ and

\det(A^{-1}) = \frac{1}{\det A}.

You may use that $\det(AB) = \det(A)\det(B)$ for all $n \times n$ matrices $A$ and $B$ .

Write your proof in plain text. Put math between dollar signs, like $x^2 \ge 0$ .

Your formatted proof appears here.

ProofProperties of the determinant

Let $A$ be an invertible $n \times n$ matrix. Prove that $\det A \neq 0$ and

\det(A^{-1}) = \frac{1}{\det A}.

You may use that $\det(AB) = \det(A)\det(B)$ for all $n \times n$ matrices $A$ and $B$ .

Write your proof in plain text. Put math between dollar signs, like $x^2 \ge 0$ .

Your formatted proof appears here.