Question

If A = $\left[\begin{array}{ccc}a& a^2& a^3-1\\ b& b^2& b^3-1\\ c& c^2& c^3-1\end{array}\right]$is a singular matrix then abc is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

For singular matrix,

|A| = 0

$\left[\begin{array}{ccc}a& a^2& a^3-1\\ b& b^2& b^3-1\\ c& c^2& c^3-1\end{array}\right]=0$


$\left[\begin{array}{ccc}a& a^2& a^3\\ b& b^2& b^3\\ c& c^2& c^3\end{array}\right]+\left|\begin{array}{ccc}a& a^2& -1\\ b& b^2& -1\\ c& c^2& -1\end{array}\right|=0$

$abc\left|\begin{array}{ccc}1& a& a^2\\ 1& b& b^2\\ 1& c& c^2\end{array}\right|-\left|\begin{array}{ccc}a& a^2& 1\\ b& b^2& 1\\ c& c^2& 1\end{array}\right|=0$
abc = 1