Calculate the determinant and multiplicative inverse of square matrices of any order, with technology.

A manufacturing company uses matrix M to represent production schedules across three factories and four product lines. M = \begin{pmatrix} 2 & 3 & 1 & 4 \\ 1 & 2 & 3 & 2 \\ 4 & 1 & 2 & 3 \end{pmatrix}\u0004 A related cost-adjustment matrix C is a 3 × 3 square matrix: C = \begin{pmatrix} 2 & 1 & 0 \\ 3 & 4 & 1 \\ 1 & 2 & 3 \end{pmatrix}\u0004 a) Calculate the determinant of matrix C. [2 marks] b) Hence, calculate the multiplicative inverse of matrix C, writing your answer in exact form. [2 marks]

Calculate the determinant of the matrix A = [[3, 1, 2], [0, -1, 4], [5, 2, -3]].

Consider the matrix \[M = \begin{pmatrix} 2 & 3 & -1 \\ 1 & -2 & 4 \\ 3 & 1 & 2 \end{pmatrix}\] (a) Calculate the determinant of \(M\), correct to 2 decimal places. (2 marks) (b) Hence, find the multiplicative inverse \(M^{-1}\), and write the answer as a matrix with entries correct to 2 decimal places. (2 marks)