Matrices are a vital mathematical tool for calculating forces, vectors, tensions, masses, loads and a myriad of other factors that must be accounted for in engineering to ensure a safe and resource-efficient structure.
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Matrices have a wider application in engineering. Many problems can be transformed in to simultaneous equation and their solution can easily be find with the help of matrices.
Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.
Matrices are used in pretty much any situation where several linear equations are involved. They're used all over the place in physics, chemistry, engineering, and economics. I linked a site below with more information.
The matrices must have the same dimensions.
Only square matrices have a determinant