Find the inverse of matrix B={(-1,-3,0),(2,4,0)(-1,-1,2)} by finding the adjoint as well as using Cayley-Hamiltion theorem?

1 Answer
Feb 5, 2018

B^(-1)=((-2/5, 3/10, 0), (1/5, 1/10, 0), (-1/10, 1/5, 1/2))

Explanation:

Cofactor matrix of B is,

Cof(B)=((8, -4, 2), (-6, -2, -4), (0, 0, -10))

Hence adjoint matrix of B,

Adj(B)=(Cof(B))^T=((8, -6, 0), (-4, -2, 0), (2, -4, -10))

Determinant of B

Det(B)=-20

Thus, inverse of B matrix is,

B^(-1)=(Adj(B))/(Det(B))=((-2/5, 3/10, 0), (1/5, 1/10, 0), (-1/10, 1/5, 1/2))