Identify the pair of non-zero matrices for which but .

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Identify the pair of non-zero 2×22\times2 matrices (A,B)(A,B) for which AB=O2AB = O_2 but BA≠O2BA \ne O_2. (a) A=[1000],  B=[0100]A=\begin{bmatrix}1&0\\0&0\end{bmatrix},\;B=\begin{bmatrix}0&1\\0&0\end{bmatrix} (b) A=[1000],  B=[0001]A=\begin{bmatrix}1&0\\0&0\end{bmatrix},\;B=\begin{bmatrix}0&0\\0&1\end{bmatrix} (c) A=[0100],  B=[1000]A=\begin{bmatrix}0&1\\0&0\end{bmatrix},\;B=\begin{bmatrix}1&0\\0&0\end{bmatrix} (d) A=[1001],  B=[0100]A=\begin{bmatrix}1&0\\0&1\end{bmatrix},\;B=\begin{bmatrix}0&1\\0&0\end{bmatrix}

Related theory

Browse the problem library