Can we multiply two matrices of any size?
Yes, it is possible to multiply two matrices of any size, provided that the number of columns in the first matrix matches the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
The multiplication of two matrices A and B is defined as follows: if A is an m×n matrix and B is an n×p matrix, then the resulting matrix C will be an m×p matrix. The value of each element cij in C is obtained by multiplying the corresponding row of A with the corresponding column of B and summing the products.
In order to perform the matrix multiplication, we calculate the dot product of each row of the first matrix with each column of the second matrix. This requires that the inner dimensions of the two matrices match (the number of columns in the first matrix equals the number of rows in the second matrix). If this condition is not satisfied, matrix multiplication is not possible.
It is important to note that matrix multiplication is not commutative, which means that the order of multiplication matters. In other words, AB is not necessarily equal to BA, unless both matrices are square matrices and the matrices commute (i.e., AB = BA).
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