Matrices & Determinants
Adjoint of Matrix
Grade 12
Question:
<p>If <i>A</i> = <span>$$\begin{bmatrix} 3 & 4 \\ 5 & 7 \end{bmatrix}$$</span>, then <i>A</i> × (adj <i>A</i>) is equal to</p>
<p>(a) <i>A</i></p>
<p>(b) |<i>A</i>|</p>
<p>(c) |<i>A</i>| <i>I</i></p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: The product of a matrix with its adjoint always equals the determinant times the identity matrix: A(adj A) = |A|I.
<p><strong>Step 1:</strong> Recall the property that <i>A</i> × (adj <i>A</i>) = |<i>A</i>| <i>I</i>, where <i>I</i> is the identity matrix.</p><p><strong>Step 2:</strong> This is a fundamental property of adjoint matrices.</p><p>∴ Answer is (c) |<i>A</i>| <i>I</i>.</p>
Correct Answer: c