MHT CET202014 Oct 2020Morning ShiftMathematicsMatricesActual
If the elements of matrix A are the reciprocals of elements of matrix [ array ccc 1 & & ² & ² & 1 ² & 1 & array ] , where is complex cube root of unity, then
Options
- AA⁻¹=I
- BA⁻¹=A²
- CA⁻¹=A
- DA⁻¹ does not exits
Correct answer
D. A⁻¹ does not exits
Step-by-step solution
aligned We have, A &= [ array ccc 1 & 1 & 1 ² 1 & 1 ² & 1 1 ² & 1 & 1 array ] | A | &=1 1 ³ -1 - 1 ( 1 ² - 1 ² )+ 1 ² ( 1 - 1 ⁴ ) &=1(1-1)-0+ 1 ² ( 1 - 1 ) [ ³=1 and ⁴= ] | A | &=0 A ⁻¹ does not exist aligned