First slide

Applications of determinant

Question

Let $A = {(a_{i j})}_{3 \times 3},$ where $a_{i j} \in C$ the set of complex numbers. If $\det (A) = 2 - 3 i,$ then $\det (A^{- 1})$ equals:

Moderate

A

$\frac{1}{13} (2 - 3 i)$
B

$\frac{1}{13} (2 + 3 i)$
C

$2 - 3 i$
D

$2 + 3 i$

Solution

$\begin{aligned} \det (A^{- 1}) = \frac{1}{\det (A)} = \frac{1}{2 - 3 i} \\ = \frac{2 + 3 i}{2^{2} + 3^{2}} = \frac{1}{13} (2 + 3 i) \end{aligned}$

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