Matrices Q/A 5: Understanding Matrix Commutativity with a 2x2 Example

Hello amazing people,
It’s another beautiful day with Mathematics! In today’s video, I’ll be using matrix multiplication on two different matrices of order 2 to determine whether they are commutative or not.
The matrices involved are Matrix P and Matrix Q. First, I multiplied P by Q (i.e., PQ) and obtained a 2x2 matrix with the elements: [7,7,2,4]

Next, I reversed the multiplication by calculating Q multiplied by P (i.e., QP). The result was also a 2x2 matrix, but this time with different elements: [3,5,2,8]

This clearly shows that Matrix P and Matrix Q are not commutative, because for two matrices of the same order, multiplication is said to be commutative only if the product remains the same regardless of the order in which the matrices are multiplied.
Kindly see the workings below;

Thanks for stopping by, and I hope this lesson is insightful and educational!

Tools Used

Graphics tablet/Pen
Miro online white board
Laptop

Video edited with VSDC

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