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Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

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$A = I A$ [row transformation]
$[\begin{array}{cc} 1 & a m p; 3 \\ 2 & a m p; 7 \end{array}] = [\begin{array}{cc} 1 & a m p; 0 \\ 0 & a m p; 1 \end{array}] A$
$R_{2} \to R_{2} - 2 R_{1}$
$[\begin{array}{cc} 1 & a m p; 3 \\ 0 & a m p; 1 \end{array}] = [\begin{array}{cc} 1 & a m p; 0 \\ - 2 & a m p; 1 \end{array}] A$
$R_{1} \to R_{1} - 3 R_{2}$
$[\begin{array}{cc} 1 & a m p; 0 \\ 0 & a m p; 1 \end{array}] = [\begin{array}{cc} 7 & a m p; - 3 \\ - 2 & a m p; 1 \end{array}] A$
$∴ A^{- 1} = [\begin{array}{cc} 7 & a m p; - 3 \\ - 2 & a m p; 1 \end{array}]$