If then (A')2 =

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If $A = [\begin{array}{cc} 2 & 3 \\ 5 & - 7 \end{array}]$ then (A')² =

$[\begin{array}{ccc} 5 & - 7 & 12 \\ 1 & 4 & 22 \end{array}]$

$[\begin{array}{cc} 1 & 17 \\ 1 & - 4 \\ 0 & 2 \end{array}]$

$[\begin{array}{cc} - 19 & - 25 \\ - 15 & 64 \end{array}]$

$[\begin{array}{cc} 19 & - 25 \\ - 15 & 64 \end{array}]$

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Given,

A = (\begin{array}{cc} 2 & 3 \\ 5 & - 7 \end{array})

\Rightarrow A^{'} = (\begin{array}{cc} 2 & 5 \\ 3 & - 7 \end{array})

Now, (A')²

= {(\begin{array}{cc} 2 & 5 \\ 3 & - 7 \end{array})}^{2}

= (\begin{array}{cc} 2 & 5 \\ 3 & - 7 \end{array}) (\begin{array}{cc} 2 & 5 \\ 3 & - 7 \end{array})

= (\begin{array}{cc} 2 \cdot 2 + 5 \cdot 3 & 2 \cdot 5 + 5 (- 7) \\ 3 \cdot 2 + (- 7) \cdot 3 & 3 \cdot 5 + (- 7) (- 7) \end{array})

= (\begin{array}{cc} 19 & - 25 \\ - 15 & 64 \end{array})

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