Question

If $A=\left[\begin{array}{cc}1& 4\\ -1& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}2& -1\\ -1& 3\end{array}\right],$ then$\left[\begin{array}{cc}4& 7\\ -3& 5\end{array}\right]$ is

• A. $2A+B$
• B. $A-B$
• C. $AB$
• D. $A-2B$

Answer 1

Answer: (A)

$2A+B$

Given , $A=\left[\begin{array}{cc}1& 4\\ -1& 1\end{array}\right],B=\left[\begin{array}{cc}2& -1\\ -1& 3\end{array}\right]$

Now, we will check all options one by one

Option A: $2A+B=\left[\begin{array}{cc}4& 7\\ -3& 5\end{array}\right]$
Option B: $A-B=\left[\begin{array}{cc}-1& 5\\ 0& -2\end{array}\right]$
Option C: $AB=\left[\begin{array}{cc}-2& 11\\ -3& 4\end{array}\right]$
Option D: $A-2B=\left[\begin{array}{cc}-3& 6\\ 1& -5\end{array}\right]$
Hence, option A will be correct.