Question:
If A is a square matrix of order 3 with determinant 4, then write the value of |−A|.
Solution:
$|A|=4$
Here,
Order of the matrix $(n)=3$
Using properties of matrices, we get
$|\mathrm{kA}|=\mathrm{k}^{\mathrm{n}}|\mathrm{A}| \quad[$ For a square matrix of order $n$ and constant $k]$
$\Rightarrow|-\mathrm{A}|=(-1)^{3}|\mathrm{~A}|=(-1) \times 4=-4$