AQA FP1 2013 June — Question 2

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
TopicMatrices

2 The matrices \(\mathbf { A }\) and \(\mathbf { B }\) are defined by $$\mathbf { A } = \left[ \begin{array} { c c } p & 2
4 & p \end{array} \right] \quad \mathbf { B } = \left[ \begin{array} { l l } 3 & 1
2 & 3 \end{array} \right]$$
  1. Find, in terms of \(p\), the matrices:
    1. \(\mathbf { A } - \mathbf { B }\);
    2. AB .
  2. Show that there is a value of \(p\) for which \(\mathbf { A } - \mathbf { B } + \mathbf { A B } = k \mathbf { I }\), where \(k\) is an integer and \(\mathbf { I }\) is the \(2 \times 2\) identity matrix, and state the corresponding value of \(k\).