Matrices & Determinants
Determinant of Special Matrices
Grade 12
Question:
<p>If <i>I</i> is a unit matrix of order 10, the determinant of <i>I</i> is equal to</p>
<p>(a) 10</p>
<p>(b) 1</p>
<p>(c) \(\frac{1}{10}\)</p>
<p>(d) 9</p>
Step-by-Step Solution
Key Concept: The determinant of the identity matrix is always 1, regardless of its order.
<p><strong>Step 1:</strong> The unit (identity) matrix <i>I</i> of order 10 has 1's on the diagonal and 0's elsewhere.</p><p><strong>Step 2:</strong> The determinant of a diagonal matrix is the product of its diagonal elements.</p><p><strong>Step 3:</strong> det(<i>I</i>) = 1 × 1 × ... × 1 (10 times) = 1.</p><p>∴ Answer is (b).</p>
Correct Answer: B