That is true, matrix multiplication is not commutative.
You can indicate the multiplication with a multiplication sign. If your matrices are "A" and "B", the product is: A x B In other words, you are indicating the product, but not actually carrying out any multiplication. Anybody who understands about matrices should know what this refers to.
Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.
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The time complexity of the Strassen algorithm for matrix multiplication is O(n2.81).
Matrix multiplication is possible by row versus column because it involves taking the dot product of the rows of the first matrix with the columns of the second matrix. Each element of the resulting matrix is computed by summing the products of corresponding entries from a row of the first matrix and a column of the second matrix. This operation aligns with the definition of matrix multiplication, where the number of columns in the first matrix must equal the number of rows in the second matrix. Thus, the row-column pairing enables systematic computation of the resulting matrix's elements.
Matrix multiplication typically refers to an operation which yields a new matrix from a pair of matrices which are already known. This is normally covered in an Algebra class or textbook.
No, a 3x5 matrix cannot be multiplied by another 3x5 matrix. For matrix multiplication to be possible, the number of columns in the first matrix must equal the number of rows in the second matrix. Since a 3x5 matrix has 5 columns and the second 3x5 matrix has 3 rows, multiplication is not defined in this case.
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If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.