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A is a square matrix such that A2 = A, then (I + A)3 - 7A is equal to

Posted by Tanushri Bhayani 1 year, 8 months ago

CBSE > Class 12 > Applied Maths

2 answers

Tanushri Bhayani 1 year, 8 months ago

Ohh' alright

0Thank You

Nishant Dogra 1 year, 8 months ago

Using the properties of matrix algebra, we can expand the expression (I + A)3 as follows: (I + A)3 = (I + A)(I + A)(I + A) = (I + A)(I2 + 2IA + A2) = (I + A)(I + 2A + A) = I2 + 3IA + 3A2 + A3 = I + 3A + 3A2 + A3 (since A2 = A) Substituting this expression into the original equation, we get: (I + A)3 - 7A = (I + 3A + 3A2 + A3) - 7A = I + 2A + 3A2 - 7A = I - 5A + 3A2 Therefore, (I + A)3 - 7A is equal to I - 5A + 3A2.

4Thank You

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