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  • Which of the following statements are True or False If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Which of the following statements are True or False
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

 

Answers (1)

False

If AB = AC => B=C

The above condition is only possible if matrix A is invertible

\\(i.e $ \vert $ A$ \vert $ $ \neq $ 0). \\ \Rightarrow $ If A is invertible, then \\$ \Rightarrow $ A\textsuperscript{-1}(AB)= A\textsuperscript{-1}(AC) \\$ \Rightarrow $ (A\textsuperscript{-1}A)B = (A\textsuperscript{-1}A)C \\$ \Rightarrow $ IB=IC \\$ \Rightarrow $ B=C

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infoexpert22

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