16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 5.2.4

Determinants

Mathematics — Linear Algebra · invertibility-determinant-2x2

Problem

Let

A

be a

2 \times 2

matrix over a field

F

. Show that

A

is invertible if and only if

\det A \neq 0

. When

A

is invertible, give a formula for

A^{-1}