If A and B are square matrix then (AB)T is 

If A and B are square matrix then (AB)T is  Correct Answer B<sup>T</sup>A<sup>T</sup>

Concept:

Transpose of a Matrix:

The new matrix obtained by interchanging the rows and columns of the original matrix is called the transpose of the matrix.

It is denoted by A′or AT

Properties of Transpose Matrix:

The transpose of a matrix is the matrix itself. ⇔ (AT)T = A

The transpose of matrix times a scalar (k) is equal to the constant times the transpose of the matrix. ⇔ (kA)T = k AT

The transpose of the sum or difference of two matrices is equivalent to the sum or difference of their transposes. ⇔ (A ± B)T = AT ± BT

The transpose of the product of two matrices is equivalent to the product of their transposes in reversed order. ⇔ (AB) T = BT AT

The determinant of a square matrix is the same as the determinant of its transpose. ⇔ |A|  = |AT|

From the above property statement 2 is the correct answer.

 

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