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If A=[1242]A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix}, then the value of K for which ∣2A∣=K∣A∣|2A| = K|A| is :

Solution

✅ Correct Option: 3

For an n×nn\times n matrix, ∣kA∣=kn∣A∣|kA|=k^n|A|.

Here AA is 2×22\times 2, so ∣2A∣=22∣A∣=4∣A∣|2A|=2^2|A|=4|A|.

Given ∣2A∣=K∣A∣|2A|=K|A|, comparing gives K=4K=4.

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