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

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

A = [(1,2,3)]

B = [-2 -1 -4]

1 Answer

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Best answer

Let us take C = AB

LHS = C’

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

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

RHS = B’A’

LHS = RHS

Hence proved.

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