If A is a square matrix of order 2 × 2 and A = 7, then value of |2 Ad…

Given

$|A|=7$

For a matrix of order $n$

$|kA|=k^n|A|$

Here $n=2$

$|2A|=2^2|A|$

$|2A|=4\times7=28$

Also

$|\text{Adj}(A)|=|A|^{n-1}$

Since $n=2$

$|\text{Adj}(A)|=|A|^{1}=7$

Now

$|2\,\text{Adj}(A)|=2^2|\text{Adj}(A)|$

$=4\times7=28$

The value is $28$.