Matrix solution software
I am trying to invert the matrix in the picture. I had done mistakes 3 times. And I heard someone in Khanacademy were saying "let computer do the hard tasks". I was trying to find better Matrix solution software online, but I am also willing to install software if it solves my problem.
I had found Matrix Calc. You know what when I had put the above matrix there then that webpage was completely unresponsive..
I found another site called SymbolLab. But the site isn't completely better for matrix. Only addition subtraction is helpful. But not inverse. Sometimes I get Illegal input in that site also.
I had found another one also: https://matrix.reshish.com/matrixMethod.php. In this page I just can deal with simple matrix (just talking about 3x3 matrix for now). But I can do simple inverse matrix in notepad I don't need them to solve simple matrix.
I don't think I should show further research about the topic.
3 answers
I recommend Sage. It is an opensource general purpose mathematics software based on Python. You can install it from the link above, or for quick computations, you can also just use their free server: https://sagecell.sagemath.org/
You can find many resources on inverting matrices in Sage online, but here is a quick example in a Sage interpreter:
sage: M = Matrix([[1, 4], [2, 3]])
sage: M
[1 4]
[2 3]
sage: M.inverse()
[3/5 4/5]
[ 2/5 1/5]
You could use Maxima. Some packages offer a GUI (Xmaxima or Wxmaxima, if I'm not mistaken), but you can use it in the terminal.
Below, an interactive terminal Maxima session in which I define and invert the twodimensional rotation matrix.
(%i3) m: matrix([cos(x), sin(x)], [sin(x), cos(x)]);
[ cos(x)  sin(x) ]
(%o3) [ ]
[ sin(x) cos(x) ]
(%i4) m^^1;
[ cos(x) sin(x) ]
[   ]
[ 2 2 2 2 ]
[ sin (x) + cos (x) sin (x) + cos (x) ]
(%o4) [ ]
[ sin(x) cos(x) ]
[    ]
[ 2 2 2 2 ]
[ sin (x) + cos (x) sin (x) + cos (x) ]
(%i5) trigsimp(%);
[ cos(x) sin(x) ]
(%o5) [ ]
[  sin(x) cos(x) ]
Note that Maxima is somewhat lazy and leaves even the most elementary trigonometric identities such as sin²(x)+cos²(x) unresolved. I used trigsimp
on the last output expression, %
, to simplify the output.
In Maxima, you can use the question mark to find help on a function or operator. For example, ? matrix
.
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I think Quintec's answer is a good one. But, just for the sake of completeness, I'll add some other options
Proprietary options

Maple ,a generalpurpose computer algebra systems (CAS) like SageMath.

MATLAB, a numerical computing language and development environment.

there is also Mathematica, another CAS similar to the 1st one
All of this programs are proprietary, but they may offer free/special licences for students and schools.
Free and Open source options
However, if you don't have to use any of them (as part of a curriculum for example) I suggest looking for their Open Source, and/or free alternatives first:
 My 1st suggestion is to go for a SageMath, since it's free, can be installed, or used on line, and it offers the additional advantage of used to python, a more versatile language, rather than a language that's dependent and restricted to the tool
And here is some others in no particular orther
 R: a programming language and free software environment for statistical computing and graphics.
 Julia: a highlevel, highperformance, dynamic programming language
 GNU Octave: a software featuring a highlevel programming language, primarily intended for numerical computations.
More
A comparative list of numericalanalysis software
https://en.wikipedia.org/wiki/Computer_algebra_system https://en.wikipedia.org/wiki/List_of_numericalanalysis_software https://en.wikipedia.org/wiki/Comparison_of_numericalanalysis_software
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