Question

If [ -2 5 7 6] and |B| = -|A|, which matrix is matrix B?

Answer 1

|A| and |B| denote the determinants of the matrices A and B.

We have

$|A| = \begin{vmatrix}-2&5\\7&6\end{vmatrix} = (-2)\times6-7\times5 = -12 - 35 = -47$

Then B is a matrix such that |B| = -|A| = +47.

The only choice satisfying this is C, since

$\begin{vmatrix}12&1\\13&5\end{vmatrix} = 12\times5-13\times1 = 60 - 13 = 47$