Q1 of 28 Page 3

If A is a square matrix such that A2 = A, then write the value of 7A – (I + A)3.

Given: A2 = A


To Find: 7A – (I + A)3


Opening the brackets, we get,


7A – (I + A)3 = 7A – (I3 + A3 + 3.I2.A + 3.I.A2)


7A – (I + A)3 = 7A – (I + A.A2 + 3A + 3A)


[Since, A2 = A and In = I]


Therefore, now we have,


7A – (I + A)3 = 7A – I – A + 6A = - I


Hence, the value of the expression is -I.


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