Let A=[3−120],B=[14−25].A=\begin{bmatrix}3 & -1\\2 & 0\end{bmatrix}, \quad B=\begin{bmatrix}1 & 4\\-2 & 5\end{bmatrix}.…

Mathematics

Problem

Let A=[3−120],B=[14−25].A=\begin{bmatrix}3 & -1\\2 & 0\end{bmatrix}, \quad B=\begin{bmatrix}1 & 4\\-2 & 5\end{bmatrix}. Answer the following: (i) Calculate the product ABAB. (ii) Calculate the product BABA. (iii) Verify that AB≠BAAB\neq BA and hence establish that matrix multiplication is not commutative in this case. (iv) Determine the matrix AB−BAAB-BA.

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