HOW TO MULTIPLY MATRICES WITH DIFFERENT DIMENSIONS

Find the product of AB and BA :

Example 1 :

Solution :

Finding the AB :

By multiplying the first row of matrix A by each column of matrix B, we get to row 1 of resultant matrix AB.

By multiplying the second row of matrix A by each column of matrix B, we get to row 2 of resultant matrix AB.

Finding the BA :

By multiplying the first row of matrix B by each column of matrix A, we get to row 1 of resultant matrix BA.

By multiplying the second row of matrix B by each column of matrix A, we get to row 2 of resultant matrix BA.

Example 2 :

Solution :

Finding the AB :

Finding the BA :

Example 3 :

Solution :

Finding the AB :

By multiplying every 2 rows of matrix A by every 2 columns of matrix B, we get to 2x2 matrix of resultant matrix AB.

Finding the BA :

By multiplying every 3 rows of matrix B by every 3 columns of matrix A, we get to 3x3 matrix of resultant matrix BA.

Example 4 :

Solution :

Finding the AB :

By multiplying every 2 rows of matrix A by every 2 columns of matrix B, we get to 2x2 matrix of resultant matrix AB.

Finding the BA :

By multiplying every 4 rows of matrix B by every 4 columns of matrix A, we get to 4x4 matrix of resultant matrix BA.

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