Problem

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

$$A = \begin{pmatrix} k & 0 & 0 \\ 4 & 2 & 3 \\ 1 & 3 & 4 \end{pmatrix}$$

where $k$ is a constant.

(a) Find, in terms of $k$, the determinant of $A$

(b) Hence determine, in terms of $k$, the matrix $A^{-1}$

(c) determine the matrix $B$

Given that

• $k = 1$

• the matrix $B$ satisfies $AB = A^T$