Question 3

# If A=$$\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}$$, then show that |2A| = 4|A|

The given matrix is

$$u=\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}$$

So 2A = 2$$\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}$$

$$= \begin{bmatrix}2 & 4\\8 & 4\end{bmatrix}$$

so L.H.S. = |2A| $$= \begin{bmatrix}2 & 4\\8 & 4\end{bmatrix}$$

= 2 x 4 - 4 x 8

= 8 - 32

= -24

Now, |A| $$= \begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}$$
= 1 x 2 - 2 x 4
= 2 - 8
= -6

So R.H.S. = 4 |A| = 4 x (-6) = -24

So L.H.S. = R.H.S.