Having much problem understanding matrix. Can someone help me out with

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Having much problem understanding matrix. Can someone help me out with an example?
 
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Matrices can do many things. What do you want to do with them?
-multiply two together
-add/subtract two
-multiply by a scalar
-find the determinant
-find the inverse
-find the adjoint
-ECT
The list goes on and on. What do you want to do?
 

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