Question

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

Answer 1

\[\left| A \right| = 4 \] 
Here, 
\[\text{ Order of the matrix }\left( n \right) = 3\] 
Using properties of matrices, we get
\[\left| kA \right| = k^n \left| A \right| \left[\text{ For a square matrix of order n and constant k }\right]\] 
\[ \Rightarrow \left| - A \right| = \left( - 1 \right)^3 \left| A \right| = \left( - 1 \right) \times 4 = - 4\]