Chapter 3.3, Problem 71E

To determine

(a)

To check:

Whether the determinant of the matrix $cA$ is $nc·\det \left(A\right)$ when $A$ is a $n\times n$ matrix and $c$ is a nonzero scalar.

To determine

(b)

To check:

Whether the determinant of $A^{-1}$ is equal to the reciprocal of the determinant of invertible matrix $A.$

To determine

(c)

To check:

Whether a unique solution exist for every b such that $A$ x = b where $A$ is an invertible $n\times n$ matrix.