Step-by-Step Solution
Key Concept: Finding the sum of diagonal elements (trace) of a matrix by identifying matrix entries a, b, c, d from given matrix relationships. The trace of matrix A = a + d represents the sum of eigenvalues and is invariant under similarity transformations.
For matrices $A = \begin{pmatrix} 4 & 1 \\ -9 & -2 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$, verify that $a + d = 2$ and $\frac{c}{b} = -9$ where entries follow from matrix relationships.
Correct Answer: 3