Show that AB ≠ BA in the following matrices: and

Engineering

Mathematics

Multiplication of Matrices

Question

Show that AB ≠ BA in the following matrices:
$A = [\begin{array}{cc} 5 & - 1 \\ 6 & 7 \end{array}]$ and $B = [\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}]$

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A = [\begin{array}{cc} 5 & - 1 \\ 6 & 7 \end{array}] B = [\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}]

AB : - [\begin{array}{cc} 5 & - 1 \\ 6 & 7 \end{array}] [\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}]

= [\begin{array}{cc} 7 & 1 \\ 33 & 34 \end{array}]

BA = [\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}] [\begin{array}{cc} 5 & - 1 \\ 6 & 7 \end{array}]

= [\begin{array}{cc} 16 & 5 \\ 39 & 25 \end{array}]

Hence AB ≠ BA.