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

Question

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

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

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

B = [(1,-3)(2,-1)]

Answer 1

Let us take C = AB

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

RHS = B’A’

LHS = RHS

Hence proved.