Question
Download Solution PDFIf A and B are two matrices such that AB = B and BA = A, then A2 + B2 is equal to
This question was previously asked in
UP TGT Mathematics 2021 Official Paper
Answer (Detailed Solution Below)
Option 3 : A + B
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UP TGT Hindi FT 1
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125 Questions
500 Marks
120 Mins
Detailed Solution
Download Solution PDFConcept:
The associative property of matrix is given by:
X (YZ) = (XY) Z ----(1)
Given:
AB = B and BA = A ----(2)
Calculation:
A2 + B2
⇒ AA + BB
⇒ A (BA) + B (AB) [using (2)]
⇒ (AB) A + (BA) B [using (1)]
⇒ BA + AB
⇒ A + B
Hence, A2 + B2 = A + B.
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