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Choose the correct option.
From the matrix equation AB = AC, it can be concluded that B = C provided:
From the matrix equation $AB = AC$, it can be concluded that $B = C$ provided:
- (a)$A$ is singular matrix
- (b)$A$ is non-singular matrix
- (c)$A$ is a symmetric matrix
- (d)$A$ is a skew symmetric matrix
Answer
Answer
Correct option: (b)
Answer: (b) $A$ is non-singular matrix
If $|A|\ne0$, $A^{-1}$ exists. Pre-multiplying $AB=AC$ by $A^{-1}$ gives $B=C$.