Maharashtra State BoardHSC Science (Electronics) 11th
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If A = [-1112301-31],B=[214302121]. State whether AB = BA? Justify your answer. - Mathematics and Statistics

Sum

If A = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)], "B" = [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`. State whether AB = BA? Justify your answer.

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Solution

AB = `[(-1, 1, 1),(2, 3, 0),(1, -3, 1)] [(2, 1, 4),(3, 0, 2),(1, 2, 1)]`

= `[(-2 + 3 + 1, -1 + 0 + 2, -4 + 2 + 1),(4 + 9 + 0, 2 + 0 + 0, 8 + 6 + 0),(2 - 9 + 1, 1 + 0 + 2, 4 - 6 + 1)]`

∴ AB = `[(2, 1, -1),(13, 2, 14),(-6, 3, -1)]`   ...(i)

BA = `[(2, 1, 4),(3, 0, 2),(1, 2, 1)][(-1, 1, 1),(2, 3, 0),(1, -3, 1)]`

= `[(-2 + 2 + 4, 2 + 3 - 12, 2 + 0 + 4),(-3 + 0 + 2, 3 + 0 - 6, 3 + 0 + 2),(-1 + 4 + 1, 1 + 6 - 3, 1 + 0 + 1)]`

∴ BA = `[(4, -7, 6),(-1, -3, 5),(4, 4, 2)]`  ...(ii)

From (i) and (ii), we get

AB ≠ BA

Concept: Matrices - Properties of Matrix Multiplication
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Determinants and Matrices
Exercise 4.6 | Q 3 | Page 94
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