Question

(b) Give an example of nonzero 2×2 matrices A, B, C such that AB=AC, but B C.

Answer 1

Answer:

Example of matrices such hat $AB = AC, B\neq C$

Step-by-step explanation:

We have two give example of 2×2 matrices such that AB = AC BUT B ≠ C.

Example:

$A =\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]\\\\B = \left[\begin{array}{ccc}1&1\\1&2\end{array}\right], C = \left[\begin{array}{ccc}1&1\\1&3\end{array}\right]$

Solving:

$AB = \left[\begin{array}{ccc}1+0&1+0\\0+0&0+0\end{array}\right] = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]$

$AC = \left[\begin{array}{ccc}1+0&1+0\\0+0&0+0\end{array}\right] = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]$

Hence, $AB = AC, B\neq C$