Question

A is a 2 2 matrix such that A$\left|\begin{array}{c}1\\ 1\end{array}\right|$ = $\left|\begin{array}{c}1\\ 2\end{array}\right|$ and $A^2$$\left|\begin{array}{c}1\\ 1\end{array}\right|$ = $\left|\begin{array}{c}1\\ 0\end{array}\right|$ . The sum of the elements of A is

• A. 1
• B. 0
• C. 2
• D. 5

Answer 1

Answer: (C)

2

Let the other two elemnts of matrix A be x and y

$A=\left(\begin{array}{cc}1& x\\ 2& y\end{array}\right)$

$A^2=AA=\left(\begin{array}{cc}1& x\\ 2& y\end{array}\right)\left(\begin{array}{cc}1& x\\ 2& y\end{array}\right)=\left(\begin{array}{cc}1+2x& x+xy\\ 2+2y& 2x+y^2\end{array}\right)$

As given elemnets of $A^2\left(\begin{array}{c}1\\ 1\end{array}\right)=\left(\begin{array}{c}1\\ 0\end{array}\right)$

Comparing the elemnts of $A^2$ we get $1+2x=1⟹x=0and2+2y=0⟹y=-1$

$\therefore A=\left(\begin{array}{cc}1& 0\\ 2& -1\end{array}\right)$

So the sum of elemts of matrix A=$1+2+0-1=2$