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A A' is always a symmetric matrix for an...

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

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`because [A A ]= (A)A=[A A]`
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Show that A' A and A A' are both symmetric matrices for any matrix A.

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric

If A and B are matrices of the same order, then A B^T-B^T A is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix

If A is a skew-symmetric matrix and n is odd positive integer, then A^n is a skew-symmetric matrix a symmetric matrix a diagonal matrix none of these

If A is a square matrix, then A A is a (a) skew-symmetric matrix (b) symmetric matrix (c) diagonal matrix (d) none of these

The inverse of a diagonal matrix is a. a diagonal matrix b. a skew symmetric matrix c. a symmetric matrix d. none of these

If [(3,5),(7,9)] is written as A + B, where A is the skew-symmetric matrix and B is the symmetric matrix, then write the matrix A.

Which of the following is a symmetric matrix? (A) a null matrix (B) a triangular matrix (C) an idenity matrix (D) a diagonal matrix

If A and B are matrices of the same order, then A B^T-B A^T is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix

If B is a symmetric matrix, write whether the matrix A B\ A^T is symmetric or skew-symmetric.

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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