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Question
A, B and C are three matrices each of order 2 × 2.
Statement (1): If A × B = A × C ⇒ B = C.
Statement (2): Cancellation law is applicable in matrix multiplication.
Options
Both the statements are true.
Both the statements are false.
Statement 1 is true and statement 2 is false.
Statement 1 is false, and statement 2 is true.
MCQ
Assertion and Reasoning
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Solution
Both the statements are false.
Explanation:
We know that,
Matrix multiplication does not satisfy the cancellation law.
∴ Statement 2 is false.
Thus, if A × B = A × C, we cannot conclude that B = C.
∴ Statement 1 is false.
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