Which of the following is true regarding the inverse of a 2×22 \times 22×2 matrix A=(abcd)A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}A=(acbd)?
It exists if det(A)=0\det(A) = 0det(A)=0
It exists if det(A)≠0\det(A) \neq 0det(A)=0
The inverse is always equal to the transpose
The inverse of the inverse is the zero matrix