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Show that AB = BA where, A = [-23-1-121-69-4],B=[13-122-130-1] - Mathematics and Statistics

Sum

Show that AB = BA where,

A = `[(-2, 3, -1),(-1, 2, 1),(-6, 9, -4)], "B" = [(1, 3, -1),(2, 2, -1),(3, 0, -1)]`

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Solution

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

= `[(-2 + 6 - 3, -6 + 6 - 0, 2 - 3 + 1),(-1 + 4 - 3, -3 + 4 - 0, 1 - 2 + 1),(-6 + 18 - 12, -18 + 18 - 0, 6 - 9 + 4)]`

= `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`  ...(1)

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

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

= `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`  ...(2)

From (1) and (2), 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 4. (i) | Page 94
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