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Matrices of any order can be added....

Matrices of any order can be added.

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**Step-by-Step Solution:** 1. **Understanding the Statement**: The statement claims that matrices of any order can be added. We need to analyze this statement to determine its validity. 2. **Definition of Matrix Addition**: Matrix addition is defined only for matrices that have the same dimensions (i.e., the same number of rows and columns). For example, a 2x3 matrix can only be added to another 2x3 matrix. 3. **Counterexample**: To illustrate this, consider two matrices: - Matrix A (2x3): ...
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. In applying one or more row operations while finding A^(-1) by elemen...

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  2. A matrix denotes a number

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  3. Matrices of any order can be added.

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

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  5. Matrices of different order cannot be subtracted.

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  6. Matrix addition is associative as well as commutative.

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  7. Matrix m ultiplication is commutative.

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

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

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

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

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

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

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

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

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

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

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

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

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