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  4. From the matrix equation A B=A C we can conclude B=C provided that

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Q. From the matrix equation $A B=A C$ we can conclude $B=C$ provided that

Matrices

Solution:

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