CUET Preparation Today
If A is square matrix such that A2 = A, then (I + A)3 - 7A is equal to: |
A I - A I 3A |
I |
Given $A^2=A$ Find $(I+A)^3$ $(I+A)^3=I^3+3I^2A+3IA^2+A^3$ $=I+3A+3A^2+A^3$ Since $A^2=A$ $A^3=A\cdot A^2=A\cdot A=A$ So $(I+A)^3=I+3A+3A+A$ $=I+7A$ Now $(I+A)^3-7A=(I+7A)-7A$ $=I$ The value is $I$ (identity matrix). |
