If A= [ array ccc 2 & 0 & 0 0 & -2 & 0 0 & 0 & -1 array ] , then A⁴ A⁻¹=

Step-by-step solution

Understand that A is a diagonal matrix A^ n = [ array ccc a₁₁^ n & 0 & 0 0 & a₂₂^ n & 0 0 & 0 & a₃₃^ n array ] A⁴= [ array ccc 16 & 0 & 0 0 & 16 & 0 0 & 0 & 1 array ] aligned Here |A| &= [ array ccc 2 & 0 & 0 0 & -2 & 0 0 & 0 & -1 array =2(2)=4 . adj A &= [ array ccc 2 & 0 & 0 0 & -2 & 0 0 & 0 & -4 array ] A⁻¹= 1 4 [ array ccc 2 & 0 & 0 0 & -2 & 0 0 & 0 & -4 array ]= [ array ccc 1 2 & 0 & 0 0 & -1 2 & 0 0 & 0 & -1 array ] A⁴ A⁻¹ &= [ array ccc 16 & 0 & 0 0 & 16 & 0 0 & 0 & 1 array ] [ array ccc 1 2 & 0 & 0 0 & -1 2