Question

If $A=\left[\begin{array}{cc}1& 0\\ 2& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}3& 4\\ -5& 2\end{array}\right]$ Find AB

• A. $\left[\begin{array}{cc}2& 5\\ 1& 10\end{array}\right]$
• B. $\left[\begin{array}{cc}3& 4\\ 1& 10\end{array}\right]$
• C. $\left[\begin{array}{cc}3& 4\\ 3& 0\end{array}\right]$
• D. $\left[\begin{array}{cc}6& 4\\ 8& 10\end{array}\right]$

Answer 1

The correct option is B

$\left[\begin{array}{cc}3& 4\\ 1& 10\end{array}\right]$

$AB=\left[\begin{array}{cc}1& 0\\ 2& 1\end{array}\right]\left[\begin{array}{cc}3& 4\\ -5& 2\end{array}\right]=\left[\begin{array}{cc}(1\times 3)+(-5\times 0)& (4\times 1)+(2\times 0)\\ (3\times 2)+(-5\times 1)& (4\times 2)+(2\times 1)\end{array}\right]=\left[\begin{array}{cc}3& 4\\ 1& 10\end{array}\right]$