1. Tardigrade
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  3. Mathematics
  4. If A=[1 0 0 -1] and B=[0 1 1 0], then

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Q. If $A=\begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}$ and $B=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$, then

Matrices

Solution:

If $A=\begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}$ and $B=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$, then $A B=\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$ and $B A=\begin{bmatrix}0 & -1 \\ 1 & 0\end{bmatrix}$ Clearly, $A B \neq B A$
Thus, matrix multiplication is not commutative.
This shows that even if $A B$ and $B A$ are of same order, then they may not be same