Compute the products AB and BA whichever exists in the following case: and

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Compute the products AB and BA whichever exists in the following case:
$A = [\begin{array}{cc} 1 & - 2 \\ 2 & 3 \end{array}]$ and $B = [\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 1 \end{array}]$

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$A = [\begin{array}{cc} 1 & - 2 \\ 2 & 3 \end{array}]$ and $B = [\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 1 \end{array}]$

In product BA number of columns in B id greater than the number of rows in A. So, BA does not exists.

\Rightarrow AB = [\begin{array}{cc} 1 & - 2 \\ 2 & 3 \end{array}] [\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 1 \end{array}]

= [\begin{array}{ccc} 1 - 4 & 2 - 6 & 3 - 2 \\ 2 + 6 & 4 + 9 & 6 + 3 \end{array}]

= [\begin{array}{ccc} - 3 & - 4 & 1 \\ 8 & 13 & 9 \end{array}]

∴ AB = [\begin{array}{ccc} - 3 & - 4 & 1 \\ 8 & 13 & 9 \end{array}]

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