JEE Main 2019 (Online) 12th April Morning ShiftQuestion 1
If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A+B=\begin{bmatrix}2&3\\5&-1\end{bmatrix}$, then $AB$ is equal to:
Matrices
Solution
$A=\frac{S+S^T}2=\begin{bmatrix}2&4\\4&-1\end{bmatrix}$, $B=\frac{S-S^T}2=\begin{bmatrix}0&-1\\1&0\end{bmatrix}$. $AB=\begin{bmatrix}4&-2\\-1&-4\end{bmatrix}$.