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For two matrices A and B , verify that (...

For two matrices `A` and `B` , verify that `(A B)^T=B^T\ A^T` , where `A=[1 3 2 4]` , `B=[1 4 2 5]`

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Given:`A=[(1, 3),( 2, 4)]`, `B=[(1, 4),( 2, 5)]`
`AB^T=([(1, 3),( 2, 4)][(1, 4),( 2, 5)])^T`
`AB^T=[(1+6,4+15),(2+8,8+20)]^T`
`AB^T=[(7,19),(10,28)]^T`
`AB^T=[(7,10),(19,28)]`
`B^TA^T=[(1,2),(4,5)][(1,2),(3,4)]`
`B^TA^T=[(1+6,2+8),(4+15,8+20)]`
`B^TA^T=[(7,10),(19,28)]`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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  14. Let A and B be symmetric matrices of same order. Then A+B is a symmetr...

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  16. Show that all positive integral powers of a symmetric matrix are sy...

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  18. A matrix which is both symmetric as well as skew-symmetric is a nul...

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  19. If A=[2 3 4 5] , prove that A-A^T is a skew-symmetric matrix.

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  20. If A=[3-4 1-1] , show that A-A^T is a skew symmetric matrix.

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