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If (AB)=BA, where A and B are not square...

If (AB)=BA, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

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To determine whether the statement "If (AB) = BA, where A and B are not square matrices, then the number of rows in A is equal to the number of columns in B and the number of columns in A is equal to the number of rows in B" is true or false, we can analyze the situation step by step. ### Step-by-Step Solution: 1. **Define the dimensions of matrices A and B**: - Let matrix A have dimensions \( m \times n \) (m rows and n columns). - Let matrix B have dimensions \( p \times k \) (p rows and k columns). ...
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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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