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?

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Answer 1 · 2018-02-05T20:42:53

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

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))#