Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?
- A. Both A and B are null matrices
- B. Either A or B is a null matrix
- C. B is a null matrix if A is a non-singular matrix ✓
- D. Both A and B are singular matrices
Correct Answer: C. B is a null matrix if A is a non-singular matrix
Explanation
If AB = 0 and A is non-singular, its inverse A^{-1} exists. Pre-multiplying by A^{-1} gives A^{-1}AB = 0, which simplifies to IB = 0, hence B = 0.
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