If A= [ array ll 2 & -1 3 & -2 array ] , then the inverse of the matrix A^3 is

Step-by-step solution

A= [ array ll 2 & -1 3 & -2 array ] aligned |A| & =-4+3=-1 adj (A) & = [ array cc -2 & -3 -(-1) & 2 array ]^T= [ array cc -2 & -3 1 & 2 array ]^T= [ array cc -2 & 1 -3 & 2 array ] A⁻¹ & = adj (A) |A| = [ array ll -2 & 1 -3 & 2 array ] (-1) = [ array cc 2 & -1 3 & -2 array ]=A A⁻¹ & =A A A⁻¹=A A I & =A^2 A I=A A^2 A & =A^3 (A)⁻¹= (A^3 )⁻¹ A & = (A^3 )⁻¹ (A^3 )⁻¹=A aligned