Question

If A=\(\begin{bmatrix}1&3\\2&1\end{bmatrix}\), then ________

(a) |2A|=4|A|

(b) |2A|=2|A|

(c) |A|=2|A|

(d) |A|=|4A|

This question was posed to me by my school teacher while I was bunking the class.

Question is from Properties of Determinants in portion Determinants of Mathematics – Class 12

Answer 1

Right choice is (a) |2A|=4|A|

Easiest explanation: Given that, A=\(\begin{bmatrix}1&3\\2&1\end{bmatrix}\)

2A=2\(\begin{bmatrix}1&3\\2&1\end{bmatrix}\)=\(\begin{bmatrix}2&6\\4&2\end{bmatrix}\)

|2A|=\(\begin{vmatrix}2&6\\4&2\end{vmatrix}\)=(4-24)=-20

4|A|=4\(\begin{vmatrix}1&3\\2&1\end{vmatrix}\)=4(1-6)=4(-5)=-20

∴|2A|=4|A|.