If A is a symmetric matrix and B is a skew-symmetrix matrix such that A + B = , then AB is equal to

Engineering

Mathematics

Symmetric and Skew Symmetric Matrices

Question

If A is a symmetric matrix and B is a skew-symmetrix matrix such that A + B = $[\begin{matrix} 2 & 3 \\ 5 & - 1 \end{matrix}]$ , then AB is equal to

$[\begin{matrix} - 4 & 2 \\ 1 & 4 \end{matrix}]$

$[\begin{matrix} 4 & - 2 \\ - 1 & - 4 \end{matrix}]$

$[\begin{matrix} 4 & - 2 \\ 1 & - 4 \end{matrix}]$

$[\begin{matrix} - 4 & - 2 \\ - 1 & 4 \end{matrix}]$

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A = A',B = –B'

$A + B = [\begin{matrix} 2 & 3 \\ 5 & - 1 \end{matrix}] . ....... (1)$

$A' + B' = [\begin{matrix} 2 & 5 \\ 3 & - 1 \end{matrix}]$

$A - B = [\begin{matrix} 2 & 5 \\ 3 & - 1 \end{matrix}] . ......... (2)$

After adding equation (1) and (2)

$A = [\begin{matrix} 2 & 4 \\ 4 & - 1 \end{matrix}], B = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]$

$AB = [\begin{matrix} 4 & - 2 \\ - 1 & - 4 \end{matrix}]$