Question

Compute the following determinant :

$\left|\begin{array}{cc}{a}^2& ab\\ ab& b^2\end{array}\right|$

Answer 1

Let A = $\left|\begin{array}{cc}{a}^2& ab\\ ab& b^2\end{array}\right|$

$\because$ determinant of a matrix $\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right|$ is

given by $a_n{a}_{22}-a_{21}{a}_{12}$

$\Rightarrow |A|=a^2{b}^2-\left(ab\right)\left(ab\right)$

$=a^2{b}^2-a^2{b}^2=0$

$\therefore |A|=0$