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Question
If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.
Options
A
I – A
I
3A
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Solution
If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to I.
Explanation:
Given: A2 = A
∵ A3 = A2. A
= A.A = A2 = A
∴ (I + A)3 – 7A = I3 + 3i2A + 3IA2 + A3 – 7A
= I3 + 3IA + 3IA2 + A3 – 7A
= I + 3A + 3A2 + A3 – 7A
= I + 3A + 3A + A2 . A – 7A
= I + 3A + 3A + A – 7A
= 7A – 7A + I
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