Algebra of Matrices — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Give example of matrices: A and B such that AB ≠ BA
✓
Answer
Let $ \text{A}=\begin{bmatrix}\text{a}&0\\0&0\end{bmatrix},\ \text{B}=\begin{bmatrix}0&\text{b}\\0&0\end{bmatrix}$ $\text{A}\text{B}=\begin{bmatrix}\text{a}&0\\0&0\end{bmatrix}\begin{bmatrix}0&\text{b}\\0&0\end{bmatrix}$ $=\begin{bmatrix}0+0&\text{a}\text{b}+0\\0+0&0+0\end{bmatrix}$ $\text{AB}=\begin{bmatrix}0&\text{a}\text{b}\\0&0\end{bmatrix}$ $\text{BA}=\begin{bmatrix}0&\text{b}\\0&0\end{bmatrix}\begin{bmatrix}0&\text{a}\\0&0\end{bmatrix}$ $ =\begin{bmatrix}0+0&0+0\\0+0&0+0\end{bmatrix}$ $ \text{BA}=\begin{bmatrix}0&0\\0&0\end{bmatrix}$ From equation (i) and (ii) AB ≠ BA When $ \text{A}=\begin{bmatrix}\text{a}&0\\0&0\end{bmatrix},\ \text{B}=\begin{bmatrix}0&\text{b}\\0&0\end{bmatrix}$
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