For each of the following pairs of matrices A and B, verify that (AB)’ = (B’ A’) : A = [(1,3)(2,4)] B = [(1,4)(2,5)]

Question

For each of the following pairs of matrices A and B, verify that (AB)’ = (B’ A’) :

A = \( \begin{bmatrix} 1&3 \\[0.3em] 2 & 4 \\[0.3em] \end{bmatrix}\) and B = \( \begin{bmatrix} 1&4 \\[0.3em] 2 & 5 \\[0.3em] \end{bmatrix}\)

A = [(1,3)(2,4)]

B = [(1,4)(2,5)]

Answer 1

Let us take C = AB

To find RHS we will find transpose of matrix A and B,

A' = \( \begin{bmatrix} 1&2 \\[0.3em] 3&4 \\[0.3em] \end{bmatrix}\) and B' = \( \begin{bmatrix} 1&2 \\[0.3em] 4&5 \\[0.3em] \end{bmatrix}\)

RHS = B’A’

LHS = RHS

Hence proved.