According to the rules of matrix multiplication, the number of columns in the first matrix must match the number of rows in the second matrix. In the case of (A+B)(A+B), the first matrix has two columns and the second matrix has two rows, which does not satisfy this rule.
Yes, it can be valid for matrices if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. This is known as the commutative property of multiplication.
The correct way to multiply two matrices is to ensure that the number of columns in the first matrix is equal to 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.
Understanding why (A+B)(A+B) is not valid for matrices is important in order to perform accurate calculations and avoid errors in linear algebra. It also helps to develop a deeper understanding of the rules and properties of matrix multiplication.
Yes, the order of multiplication can be changed in matrix multiplication. This is known as the associative property of multiplication. However, the resulting matrix will still have the same dimensions as the original matrices.