Question

For which values of a, b, c, and d will$A=\left[\begin{array}{cc}a& b\\ c& d\\ & \end{array}\right]=A^{-1}$?

Short answer

The obtained values are $a=1$, $b=0$, $c=1$ and $d=0$.

Step-by-step solution

Step 1- Determine the approach that can be used

The identity matrix $\left[\begin{array}{cc}1& 0\\ 0& 1\\ & \end{array}\right]$can have the inverse that is also an identity matrix.

– Determine the value of a, b, c and d by using the approach 

Use the obtained approach and determine the value of a, b, c and d.

The obtained values are$a=1$, $b=0$, $c=1$ and $d=0$.

Step 3- Make the conclusion

As the inverse of an identity matrix$\left[\begin{array}{cc}1& 0\\ 0& 1\\ & \end{array}\right]$will be $\left[\begin{array}{cc}1& 0\\ 0& 1\\ & \end{array}\right]$so obtained values are correct.