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Matrix multiplication is
- a)Associative but not commutative
- b)Commutative but not associative
- c)Associative as well as commutative
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Matrix multiplication isa)Associative but not commutativeb)Commutative...
Matrix multiplication is associative but not commutative. ans should be A.
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Matrix multiplication isa)Associative but not commutativeb)Commutative...
Understanding Matrix Multiplication
Matrix multiplication is a fundamental operation in linear algebra, but it does not behave like regular multiplication of numbers. It is important to understand its properties, particularly regarding associativity and commutativity.
Associativity of Matrix Multiplication
- Matrix multiplication is associative. This means that for any three matrices A, B, and C, the equation (AB)C = A(BC) holds true, provided the dimensions are compatible for multiplication.
- This property allows us to group matrices in any manner without affecting the final product, making computations easier and more flexible.
Commutativity of Matrix Multiplication
- Matrix multiplication is not commutative. This means that, in general, AB ≠ BA for two matrices A and B.
- The order of multiplication matters; switching the order of the matrices can lead to different results. This is particularly evident with non-square matrices or when the dimensions do not align.
Conclusion
- In summary, matrix multiplication is associative but not commutative.
- Thus, the correct answer to the question is option D: Associative but not commutative.
Understanding these properties is crucial for anyone studying linear algebra, as they influence how matrices can be manipulated in various mathematical contexts.
Matrix multiplication is a fundamental operation in linear algebra, but it does not behave like regular multiplication of numbers. It is important to understand its properties, particularly regarding associativity and commutativity.
Associativity of Matrix Multiplication
- Matrix multiplication is associative. This means that for any three matrices A, B, and C, the equation (AB)C = A(BC) holds true, provided the dimensions are compatible for multiplication.
- This property allows us to group matrices in any manner without affecting the final product, making computations easier and more flexible.
Commutativity of Matrix Multiplication
- Matrix multiplication is not commutative. This means that, in general, AB ≠ BA for two matrices A and B.
- The order of multiplication matters; switching the order of the matrices can lead to different results. This is particularly evident with non-square matrices or when the dimensions do not align.
Conclusion
- In summary, matrix multiplication is associative but not commutative.
- Thus, the correct answer to the question is option D: Associative but not commutative.
Understanding these properties is crucial for anyone studying linear algebra, as they influence how matrices can be manipulated in various mathematical contexts.
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Matrix multiplication isa)Associative but not commutativeb)Commutative but not associativec)Associative as well as commutatived)None of theseCorrect answer is option 'D'. Can you explain this answer?
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