The question is an illustration of matrix determinants.
The true statement is (b) [tex]\mathbf{|A| = -|B|}[/tex]
The matrices are given as:
[tex]A = \left[\begin{array}{ccc}3&-1&5\\2&9&3\\5&3&1\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}5&3&1\\2&9&3\\3&-1&5\end{array}\right][/tex]
Next, calculate the determinants
[tex]\mathbf{|A| = 3(9\times 1 - 3 \times 3) + 1(2 \times 1 - 3 \times 5) + 5(2 \times 3 - 9 \times 5)}[/tex]
[tex]\mathbf{|A| = -208}[/tex]
[tex]\mathbf{|B| = 5(9\times 5 + 3 \times 1) - 3(2 \times 5 - 3 \times 3) + 1(2 \times -1 - 9 \times 3)}[/tex]
[tex]\mathbf{|B| = 208}[/tex]
Substitute [tex]\mathbf{|B| = 208}[/tex] in [tex]\mathbf{|A| = -208}[/tex]
[tex]\mathbf{|A| = -|B|}[/tex]
Hence, the true statement is (b) [tex]\mathbf{|A| = -|B|}[/tex]
Read more about matrix determinants at:
https://brainly.com/question/4470545
