UPSC NDA Math Model Paper 10

Given, A and B be matrices of order 3 × 3.
|AB| = 0,
We know that |AB| = |A||B|
⇒ |A||B| = 0
⇒ either |A| = 0 or |B| = 0 or both |A| = |B| = 0.
⇒ either |A| = 0 or |B| = 0 .
Hence, if A and B be matrices of order 3 × 3. If AB = 0, either |A| = 0 or |B| = 0.