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If A and B are two matrices of the same order , then A-B=B-A.

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If A and B are square matrices of the same order , then (i) (AB) = ……… (ii) (kA) ' = …….. (iii) [k(A-B)]' =…… k is any scalar)

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If A and B are symmetric matrices of the same order , then show that AB is symmetric if and only if A and B commute , that is AB=BA.

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KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (True /False)
  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 can not be subtracted .

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  5. Matrix addition is associative as well as commutative.

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  6. Matrix multiplication is commutative .

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  7. A square matrix where every element is unity is called an identity mat...

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

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

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  10. If matrix AB=O , then A=O or B=O or both A and B are null matrices .

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

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  12. If A and B are two square matrices of the same order , then AB=Ba.

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

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

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

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  16. If A , B and C are square matrices of same order, then AB=AC always i...

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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):}]andB=[{:(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. (AB)^(-1)=A^(-1)*B^(-1) , where A and B are invertible matrices satisf...

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