(a) Define the adjugate of a square matrix and write the relation between the adjugate and the inverse of an invertible matrix.
(b) Explain why the existence of an inverse for the coefficient matrix A of a linear system AX=Y guarantees that the system has exactly one solution.
(c) Consider the matrix
A=123246369.
(i) Calculate det(A).
(ii) Using your result, comment on the number of solutions the system AX=Y can have for an arbitrary column vector Y.