Answer:

Explanation:
Given matrix
![A=\left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/ihwmmo9xfw2ktecawsyue45qcsprdal1x9.png)
And
![B=\left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/rkg3yuqd4y7ahcaha3pyhyulwss1cfxao5.png)
We need to find the value of
, that will make
.
Let us find
![AB=\left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]* \left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/nuwyjm0jukb5cvmeak8qt761qrywml3o1i.png)
![AB=\left[\begin{array}{ccc}4&16+2k\\-6&-4+2k\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/nsopc8frm6co8qdl6htkztp1a6g9o1j1m0.png)
Now, let us find

![BA=\left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]* \left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/f92vlfef9648v4tlu196sgzhym1lls1dbx.png)
![BA=\left[\begin{array}{ccc}4&12\\-8-k&-4+2k\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/mihlymox49tmyno8o2to8e1l4zx969e031.png)
Put

![\left[\begin{array}{ccc}4&16+2k\\-6&-4+2k\end{array}\right]=\left[\begin{array}{ccc}4&12\\-8-k&-4+2k\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/r6lu9h6vxe72qa8f7l4x5nwz4z92789qm7.png)
In order to make
, the
should be equal. As other two values are equal that are

By solving each equation

And

We can see if the value
then
