Matrix multiplication is a fundamental operation in linear algebra and has numerous applications in various fields of science, engineering, and computation. Multiplying matrices may seem complicated at first, but with these six steps, you’ll learn how to do it easily and effectively.

Step 1: Understand Matrix Multiplication

Matrix multiplication involves taking two matrices ‘A’ and ‘B’ and producing a new matrix ‘C’. It is different from element-wise multiplication, where each element of the matrices is independently multiplied. In matrix multiplication, the elements of the resulting matrix ‘C’ are obtained by multiplying rows from matrix ‘A’ by columns from matrix ‘B’.

Step 2: Check for Matrix Compatibility

Before multiplying two matrices, you must ensure they are compatible. To do this, confirm that the number of columns in matrix ‘A’ is equal to the number of rows in matrix ‘B’. For example, a 2×3 matrix can be multiplied by a 3×4 matrix, while a 2×3 matrix cannot be multiplied by a 2×4 matrix.

Step 3: Set Up Your Workspace

Write both matrices with enough space between them to perform the multiplication. Keep track of elements from both matrices since you will need them while calculating the result. Label your matrices as ‘A’ and ‘B’, making it easier to follow through with the calculations.

Step 4: Multiply Rows by Columns

Starting with the first row in matrix ‘A’ and the first column in matrix ‘B’, multiply corresponding elements between the row and the column. For example:

A[row i]: [a1, a2, a3]

B[col j]: [b1, b2, b3]

Multiply corresponding elements:

(a1 * b1) + (a2 * b2) + (a3 * b3)

Step 5: Sum the Products

After multiplying the elements, add their products together. This value will be the element of the resulting matrix ‘C’ at position C[i][j], where ‘i’ represents the row number and ‘j’ represents the column number. Note that matrix ‘C’ will have the same number of rows as matrix ‘A’ and the same number of columns as matrix ‘B’.

Step 6: Repeat for All Elements

Repeat steps 4 and 5 for every combination of rows from matrix ‘A’ and columns from matrix ‘B’. When you finish, you’ll have your resulting matrix ‘C’ after the multiplication.

With these six steps, you can now confidently multiply matrices for any application that requires it. Keep practicing to become more comfortable with matrix multiplication and tackle even more complex linear algebra problems.