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If A and B are symmetric matrices, then ...

If A and B are symmetric matrices, then
(i) AB-BA is a ..........
(ii) BA-2AB is a.............

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To solve the problem, we need to determine the nature of the matrices \( AB - BA \) and \( BA - 2AB \) given that \( A \) and \( B \) are symmetric matrices. ### Step-by-Step Solution: **Step 1: Analyze \( AB - BA \)** 1. **Take the transpose of \( AB - BA \)**: \[ ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. If A and B are square matrices of the same order, then (i) (AB)=.......

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  2. If A is a skew-symmetric, then kA is a...........(where, k is any scal...

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  3. If A and B are symmetric matrices, then (i) AB-BA is a .......... ...

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  4. If A is symmetric matrix, then B'AB is............

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  5. If A and B are symmetric matrices of same order, then AB is symmetric ...

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  6. In applying one or more row operations while finding A^(-1) by elemen...

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  7. A matrix denotes a number

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  8. Matrices of any order can be added.

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

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  10. Matrices of different order cannot be subtracted.

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  11. Matrix addition is associative as well as commutative.

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  12. Matrix m ultiplication is commutative.

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

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

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

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  16. 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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  17. Transpose of a column matrix is a column matrix.

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

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

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

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