Question

If in the multiplication of $\left[\begin{array}{cc}a& b\\ -b& a\end{array}\right]$ and $\left[\begin{array}{cc}c& d\\ -d& c\end{array}\right],$ $A$ and $B$ are the elements of the first row, then the elements of the second row will be

• A. $B,A$
• B. $A,B$
• C. $-B,A$
• D. $B,-A$

Answer 1

The correct option is C $-B,A$


$A$ $B$
$\downarrow$ $\downarrow$
Consider, $\left[\begin{array}{cc}a& b\\ -b& a\end{array}\right]\left[\begin{array}{cc}c& d\\ -d& c\end{array}\right]=\left[\begin{array}{cc}ac-bd& ad+bc\\ -bc-ad& -bd+ac\end{array}\right]$
$\uparrow$ $\uparrow$
$-B$ $A$
Hence, the elements of the second row are $-B,A$