Q65 of 307 Page 5

Give examples of matrices

A, B and C such that AB = AC but B ≠ C, A ≠ O.

We need to find matrices A, B and C such that AB = AC but B ≠ C, A ≠ O.

Let, and.


First, we will find AB.






Now, we will find AC.






Thus, AB = AC but B ≠ C, A ≠ O when, and.


More from this chapter

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65

Give examples of matrices

A and B such that AB = O but A ≠ O, B ≠ O.

 65

Give examples of matrices

A and B such that AB = O but BA ≠ O.

 66

Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?

 67

If A and B are square matrices of the same order, explain, why in general

(i) (A + B)2 ≠ A2 + 2AB + B2


(ii) (A – B)2 ≠ A2 – 2AB + B2


(iii) (A + B)(A – B) = A2 – B2