Question

The value of $\left|\begin{array}{cc}2+i& 2-i\\ 1+i& 1-i\end{array}\right|$ is:

• A. $A$ complex quantity
• B. real quantity
• C. $0$
• D. cannot be determined

Answer 1

Answer: (A)

$A$ complex quantity

Let $A=\left|\begin{array}{cc}2+i& 2-i\\ 1+i& 1-i\end{array}\right|$
$detA=(2+i)(1-i)-(2-i)(1+i)$
$=2-2i+i-i^2-(2+2i-i-i^2)$
$=3-i-(3+i)=-2i$
$\Rightarrow detA=-2i\Rightarrow A$ complex quantity.