Matrices basics
A matrix is a rectangular grid of numbers, and you add or subtract two matrices of the same size by combining matching entries, the same way you would with vectors: if two matrices both have an entry in the same position, say 3 and 5, the sum matrix has 3 + 5 = 8 there. Matrix multiplication works differently: to multiply two matrices, you multiply each row of the first by each column of the second and add the products, which only works when the number of columns in the first matrix matches the number of rows in the second; matrices are commonly used to represent and solve systems of linear equations, and to describe transformations like rotations and reflections.
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