Question

From the matrix equation $AB=AC$ we can conclude $B=C$ provided that

• A. $A$ is non-singular
• B. $A$ is singular
• C. $A$ is symmetric
• D. $A$ is square

Answer 1

Answer: (A)

$AB=AC\Rightarrow A^{-1}AB=A^{-1}AC\Rightarrow B=C$
$A^{-1}$ exist only if $|A|\ne 0$