MCQ
If $A$ is a square matrix such that $A^2=A$, then $(I+A)^3-7 A$ is equal to
- AI - A
- B3A
- CA
- D1
(d) I
Explanation: Given that $A^2=A$
Calculating value of $(I+A)^3-7 A$ :
$
\begin{array}{l}
(I+A)^3-7 A=I^3+A^3+3 I^2 A+3 I A^2-7 A \\
=I+A^2 \cdot A+3 A+3 A+3 A^2-7 A\left(I^n=I \text { and } I \cdot A=A\right) \\
=I+A \cdot A+3 A+3 A-7 A\left(A^2=A\right) \\
=I+A+3 A+3 A-7 A
\end{array}
$
Hence, $(I+A)^3-7 A=I$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.