OCR FP1 2011 January — Question 5 3 marks

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMatrices
TypeProperties of matrix operations
DifficultyModerate -0.8 This is a straightforward matrix algebra manipulation requiring knowledge of inverse properties: (AB)^{-1} = B^{-1}A^{-1}. The simplification involves only 2-3 steps of applying standard rules with no conceptual difficulty or problem-solving required. While it's Further Maths content, it's a routine drill exercise testing basic matrix manipulation skills.
Spec4.03p Inverse properties: (AB)^(-1) = B^(-1)*A^(-1)

5 Given that \(\mathbf { A }\) and \(\mathbf { B }\) are non-singular square matrices, simplify $$\mathbf { A B } \left( \mathbf { A } ^ { - 1 } \mathbf { B } \right) ^ { - 1 } .$$

Question 5:
AnswerMarks Guidance
AnswerMarks Guidance
B1\((A^{-1})^{-1} = A\) seen or implied
M1Use product inverse correctly
\(A^2\)A1cao 3 Obtain correct answer
## Question 5:

| Answer | Marks | Guidance |
|--------|-------|----------|
| | B1 | $(A^{-1})^{-1} = A$ seen or implied |
| | M1 | Use product inverse correctly |
| $A^2$ | A1cao **3** | Obtain correct answer |

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5 Given that $\mathbf { A }$ and $\mathbf { B }$ are non-singular square matrices, simplify

$$\mathbf { A B } \left( \mathbf { A } ^ { - 1 } \mathbf { B } \right) ^ { - 1 } .$$

\hfill \mbox{\textit{OCR FP1 2011 Q5 [3]}}