1.4.7: Verification of the transpose

Transpose of a matrix

A matrix which is obtained by interchanging all the rows and columns of a given matrix is called its transpose. The transpose of a matrix A is written as At. .

Verification of the result (AB)t = At Bt

For verifying the result (AB)t = AtBt .It is necessary that AB must exists i.e A & B are conformable for multiplication. This is possible only, when number of columns in A must be equal to the number of rows in B. Now we choose matrices of suitable order/orders so that their multiplication becomes possible then try to verify the above law, (AB)t that is , transpose of a product of matrices is equal to the product of their transposes but in the reverse order.

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