Matrices & Determinants
Properties of Non-singular Matrices
Grade 12
Question:
<p>If <i>m</i> = 2 and <i>n</i> = 5, then <i>p</i> equals to</p>
<p>(a) 30</p>
<p>(b) 31</p>
<p>(c) 33</p>
<p>(d) 81</p>
Step-by-Step Solution
Key Concept: Apply the power relation for non-singular commuting matrices where AB = BA.
<p>Given: <i>m</i> = 2 and <i>n</i> = 5</p><p>Using the relation from Q. 47 or based on properties of non-singular matrices with commutativity and power relations: <i>p</i> = <i>m</i><sup><i>n</i></sup> - 1 = 2<sup>5</sup> - 1 = 32 - 1 = 31</p>
Correct Answer: b