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Question
If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to
Options
A
1 – A
1
3A
MCQ
Solution
1
Explanation:
(I + A)3 – 7A = I3 + A3 + 3I2A + 3A2I – 7A
= 1 + A3 + 3A + 3A2 – 7A
= 1 + A2, A + 3A + 3A – 7A
= 1 + A, A – A
= 1 + A2 – A
= 1 + A – A = 1
∴ (1 + A)3 – 7A = 1
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