Q. 3

# If A is a square

Given: A2 = A

To find 7A - (I + A)3

Using (a + b)3 = a3 + b3 + 3a2b + 3ab2

7A – (I + A)3 = 7A – (I3 + A3 + 3(I)2A + 3(I)A2)

7A – (I + A)3 = 7A – (I3 + A2A + 3I2A + 3IA2)

As I is identity matrix I3 = I and given A2 = A

7A – (I + A)3 = 7A – (I + AA + 3A + 3A)

7A – (I + A)3 = 7A – (I + A2 + 6A)

7A – (I + A)3 = 7A – (I + A + 6A)

7A – (I + A)3 = 7A – (I + 7A)

7A – (I + A)3 = 7A – I – 7A

7A – (I + A)3 = –I

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