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

Answer: (E)

$A=\left|\begin{array}{ccc}8& 27& 125\\ 2& 3& 5\\ 1& 1& 1\end{array}\right|$
$=8(3-5)-27(2-5)+125(2-3)$
$=8(-2)-27(-3)+125(-1)$
$=-16+81-125$
$=-60$
$\therefore A^2=(-60{)}^2=3600$