If A = [(2,-3,5)(0,7,-4)] , verify that (A’)’ = A.

Question

If A = \( \begin{bmatrix} 2 & -3& 5 \\[0.3em] 0 & 7 & -4\\[0.3em] \end{bmatrix},\) verify that (A’)’ = A.

A = [(2,-3,5)(0,7,-4)]

Answer 1

Transpose of a matrix is obtained by interchanging the rows and the columns of matrix A. It is denoted by A’.

e.g. A¹² = A²¹

A = \( \begin{bmatrix} 2 &-3 & 5 \\[0.3em] 0& 7 & -4\\[0.3em] \end{bmatrix}\)

Hence transpose of matrix A is,

A' = \( \begin{bmatrix} 2 &0 \\[0.3em] -3& 7 \\[0.3em] 5&-4 \end{bmatrix}\)

(A')' = A 

Hence, Proved.