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Matrix addition is associative as well a...

Matrix addition is associative as well as commutative.

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To determine whether the statement "Matrix addition is associative as well as commutative" is true or false, we can analyze the definitions of associative and commutative properties in the context of matrix addition. ### Step-by-Step Solution: 1. **Understanding Associative Property**: - The associative property states that for any three matrices \( A \), \( B \), and \( C \) of the same order, the following holds: \[ (A + B) + C = A + (B + C) ...
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If * is a binary operation in N defined as a*b =a^(3)+b^(3) , then which of the following is true : (i) * is associative as well as commutative. (ii) * is commutative but not associative (iii) * is associative but not commutative (iv) * is neither associative not commutative.

Consider the binary operations ** \: R\ xx\ R -> R and o\ : R\ xx\ R -> R defined as a **\ b=|a-b| and aob=a for all a,\ b\ in R . Show that ** is commutative but not associative, o is associative but not commutative.

Consider the binary operations *: RxxR->R and o: RxxR->R defined as a*b=|a-b| and aob=a for all a ,\ b in Rdot Show that * is commutative but not associative, o is associative but not commutative.

The binary operation * defined on N by a*b= a+b+a b for all a ,\ b in N is (a) commutative only (b) associative only (c) commutative and associative both (d) none of these

In the following questions a statement of assertion (A) is followed by a statement of reason ( R). A : The addition of two vectors vecP and vecQ is commutative R: By triangle law of vector addition we can prove vecP+vecQ=vecQ+vecP .

Let * be a binary operation on R defined by a*b=a b+1 . Then, * is commutative but not associative associative but not commutative neither commutative nor associative (d) both commutative and associative

Let * be a binary operation on R defined by a*b= a b+1 . Then, * is (a)commutative but not associative (b)associative but not commutative (c)neither commutative nor associative (d) both commutative and associative

On Z an operation * is defined by a*b= a^2+b^2 for all a ,\ b in Z . The operation * on Z is (a)commutative and associative (b)associative but not commutative (c) not associative (d) not a binary operation

Let *, be a binary operation on N, the set of natural numbers defined by a*b = a^b , for all a,b in N . is * associative or commutative on N?

Determine whether * on N defined by a * b=1 for all a ,\ b in N is associative or commutative?

NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. A matrix denotes a number

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  2. Matrices of any order can be added.

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  3. Two matrices are equal. If they have same number of rows and same numb...

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  4. Matrices of different order cannot be subtracted.

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  5. Matrix addition is associative as well as commutative.

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  6. Matrix m ultiplication is commutative.

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  7. A square m atrix where every element is unity is called an identity ma...

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  8. If A and B are two square matrices of the same order, then A+B=B+A.

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  9. If A and B are two m atrices of the same order, then A-B=B-A.

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  10. If A dn B be 3xx3 matrices the AB=0 implies (A) A=0 or B=0 (B) A=0 and...

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  11. Transpose of a column matrix is a column matrix.

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  12. If A and B are square matrices of the same order such that A B=B A , t...

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  13. If each of the three matrices of the same order are symmetric, then th...

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  14. If A and B are any two matrices of the same order, then (AB)=A'B'

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  15. If (AB)=BA, where A and B are not square matrices, then number of rows...

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  16. Let A; B; C be square matrices of the same order n. If A is a non sing...

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  17. A A' is always a symmetric matrix for any matrix A.

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  18. If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then AB and ...

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  19. If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

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  20. If A; B are invertible matrices of the same order; then show that (AB)...

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