Question: If A=\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\), then show that |2A| = 4|A|

Answer:

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.

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Question: If A=\(\begin{bmatrix}1 & 2\\4 & 2\end{bmatrix}\), then show that |2A| = 4|A|

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