Question

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

• A. A
• B. I − A
• C. I
• D. 3A

Answer 1

Answer: (C)

I

Answer 2

(I+A)3-7A =I3+A3+3I2A+3A2I-7A

=I+A3+3A+3A2-7A

=I+A2.A+3A+3A-7A [A2=A]

=I+A2-A

=I+A-A

=I

$\therefore$ (I+A)3-7A=I