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(C) Given that $A^2 = A$ and $I$ is the identity matrix.We need to evaluate the expression $(I + A)^2 - 3A$.Expanding the expression using the propert

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$I$

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(C) Given that $A^2 = A$ and $I$ is the identity matrix.We need to evaluate the expression $(I + A)^2 - 3A$.Expanding the expression using the property $(I + A)^2 = I^2 + IA + AI + A^2$:Since $IA = AI = A$ and $I^2 = I$,we have:$(I + A)^2 = I + A + A + A^2$$(I + A)^2 = I + 2A + A^2$Substitute $A^2 = A$ into the expression:$(I + A)^2 = I + 2A + A = I + 3A$Now,substitute this back into the original expression:$(I + A)^2 - 3A = (I + 3A) - 3A$$(I + A)^2 - 3A = I$Therefore,the correct option is $C$.

If $A$ is a square matrix such that $A^2 = A$,then $(I + A)^2 - 3A =$ . . . . . . .

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