Inverse of Parameterized 2×2 Matrix with Constraints
Consider the 2×2 matrix \(A = \begin{pmatrix} a & 2 \\ 3 & 4 \end{pmatrix}\) where \(a\) is a real parameter. (a) Express \(A^{-1}\) in terms of \(a\), assuming the inverse exists. (b) Determine the range of values for \(a\) for which the matrix \(A\) is invertible.