Matrix multiplication is a way to combine two groups of numbers. These groups, called matrices, are like big grids of numbers. To multiply them, a key rule says the first matrix's columns must match the second's rows. If this rule is followed, the new matrix gets its rows from the first and columns from the second. Mathematicians often write 'AB' for the product of matrix A and matrix B.
Jacques Binet, a French mathematician, first described this idea in 1812. It is a main tool in linear algebra, a math area that helps describe straight-line changes. For example, it shows how shapes move or transform in geometry. Matrix multiplication is very useful across many fields. Physics uses it to understand forces and movements. Economists use it to model how markets work. Engineers rely on it for designing structures or creating computer graphics. Even complex computer programs use this special math.
To multiply, you combine a row from the first matrix with a column from the second. You multiply the numbers that line up in corresponding spots. Then you add all those multiplied results together. This sum gives you one single number for the new matrix.
