Question

If $A=\left|\begin{array}{ccc}8& 27& 125\\ 2& 3& 5\\ 1& 1& 1\end{array}\right|$, then the value of $A^2$ is equal to

• A. $0$
• B. $36$
• C. $64$
• D. $2400$
• E. $3600$

Answer 1

The correct option is E $3600$

$A=\left|\begin{array}{ccc}8& 27& 125\\ 2& 3& 5\\ 1& 1& 1\end{array}\right|$
$=8(3-5)-27(2-5)+125(2-3)$

$=8(-2)-27(-3)+125(-1)$

$=-16+81-125$
$=-60$
$\therefore A^2={(-60)}^2=3600$