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5. Algebra of Matrices
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Q70 of 307 Page 5

Let and

Verify that AB = AC though B ≠ C, A ≠ 0.

Given, and.


We need to verify that AB = AC.


Let us evaluate the LHS and the RHS one at a time.


We will first calculate AB.






Now, the RHS is AC.






Thus, AB = AC even though B ≠ C and A ≠ O.


More from this chapter

All 307 →
68

Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.

69

If A and B are square matrices of the same order such that AB = BA, then show that (A + B)2 = A2 + 2AB + B2.

71

Three shopkeepers, A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill.

72

The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs 8.30, Rs 3.45 and Rs 4.50 each respectively. Find the total amount the store will receive from selling all the items.

Questions · 307
5. Algebra of Matrices
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