If and find A(BA).

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If $A = [\begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array}]$ and $B = [\begin{array}{cc} 2 & 1 \\ 1 & 2 \end{array}]$ find A(BA).

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Given

A = [\begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array}]

and

B = [\begin{array}{cc} 2 & 1 \\ 1 & 2 \end{array}]

BA = [\begin{array}{cc} 2 & 1 \\ 1 & 2 \end{array}] [\begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array}]

= [\begin{array}{cc} 2 + 2 & 1 + 4 \\ 4 + 1 & 2 + 2 \end{array}]

= [\begin{array}{cc} 4 & 5 \\ 5 & 4 \end{array}]

A (BA) = [\begin{array}{cc} 1 & 2 \\ 2 & 1 \end{array}] [\begin{array}{cc} 4 & 5 \\ 5 & 4 \end{array}]

= [\begin{array}{cc} 4 + 10 & 5 + 8 \\ 8 + 5 & 10 + 4 \end{array}]

= [\begin{array}{cc} 14 & 13 \\ 13 & 14 \end{array}]

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