Matrices & Determinants
Properties of Non-singular Matrices
Grade 12
Question:
<p>The relation between <i>m</i>, <i>n</i> and <i>p</i> is</p>
<p>(a) p = mn</p>
<p>(b) p = mn - 1</p>
<p>(c) p = nm - 1</p>
<p>(d) p = m<sup>n</sup> - 1</p>
Step-by-Step Solution
Key Concept: For commuting non-singular matrices with power relations, the combined exponent follows p = m^n - 1.
<p>For non-singular matrices A and B such that AB = BA, B<sup>n</sup> = I, and A<sup>m</sup> = I, the relation between the powers follows: <i>p</i> = <i>m</i><sup><i>n</i></sup> - 1</p><p>This can be verified by substituting values from question 46.</p>
Correct Answer: d