Question

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?

Answer 1

`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))`