If A is a square matrix of order 3 with determinant 4, then write the value of |−A|.

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 $k]$

$\Rightarrow|-\mathrm{A}|=(-1)^{3}|\mathrm{~A}|=(-1) \times 4=-4$

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