Easy -1.8 This is a straightforward matrix multiplication exercise requiring only computation of AB and BA to show they differ. The matrices are simple (2×2 with manageable numbers), and the task is purely mechanical verification rather than problem-solving or proof construction. Well below average difficulty for Further Maths.
Matrices A and B are given by \(\mathbf{A} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) and \(\mathbf{B} = \begin{pmatrix} \frac{5}{13} & -\frac{12}{13} \\ \frac{12}{13} & \frac{5}{13} \end{pmatrix}\).
Use A and B to disprove the proposition: "Matrix multiplication is commutative". [2]
Matrices A and B are given by $\mathbf{A} = \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$ and $\mathbf{B} = \begin{pmatrix} \frac{5}{13} & -\frac{12}{13} \\ \frac{12}{13} & \frac{5}{13} \end{pmatrix}$.
Use A and B to disprove the proposition: "Matrix multiplication is commutative". [2]
\hfill \mbox{\textit{SPS SPS FM 2023 Q1 [2]}}