If M is square matrix such that , then is equal to

JEE MainMathematicsToughMatrix and determinants

If M is square matrix such that $M^{2} = M$ , then
$(I + M)^{3} - 7M$ is equal to

Show answer and solution

(I + M)^{3} - 7M = (I + M)(I + M)(I + M) - 7M

= (I + M + M + M^{2})(I + M) - 7M

= I + 2M + M^{2} + M + 2M^{2} + M^{3} - 7M

= 3M^{2} + M^{3} - 4M + I

= 3M + m^{2} - 4M + I

= 3M + M - 4M + I

= I

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

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