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Compute the Indicated Products: `[[A B],[-b A]][[A -b],[B A]]` - Mathematics

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Question

Compute the indicated products:

`[[a    b],[-b      a]][[a     -b],[b         a]]`

Sum
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Solution

`[[a    b],[-b      a]][[a     -b],[b         a]]`

`⇒ [[a xx axx+b+b             axx(-b)+bxxa],[(-b)xxa+axxb            (-b)xx(-b)+axxa]]`

`⇒[[a^2+b^2            -ab^2+ab],[-ab+ab           b^2+a^2]]`

`⇒[[a^2+b^2       0],[0             a^2+b^2]]`

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Chapter 5: Algebra of Matrices - Exercise 5.3 [Page 41]

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RD Sharma Mathematics [English] Class 12
Chapter 5 Algebra of Matrices
Exercise 5.3 | Q 1.1 | Page 41
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