devarshi-dt-logo

Question:

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

Solution:

Given A² = A
7A − (I + A)³ = 7A − (I + A)(I + 2A + A²) = 7A − (I + A)(I + 3A) = 7A − (I + 4A + 3A²) = 7A − I − 4A − 3A = 7A − I − 4A − 3A = 0A − I = −I