Answer :

As, A =


A2 =


Using matrix multiplication method we can write it as-


A2 =


A2 =


A2 – 5A + 4I =


A2 – 5A + 4I =


A2 – 5A + 4I =


A2 – 5A + 4I =


Now we need to find X such that -


A2 – 5A + 4I + X = 0



X =


X =


OR


As we know that transpose of a matrix is given by interchanging rows with respective columns.


A’ = AT =


Inverse of any matrix(say B) is given by:


B-1 =


Assume, B =


Determinant of B = |B| =


Expanding about first row-


|B| = 1(-1-8)-0(-2-6)-2(-8+3)


|B| = -9+10 = 1


Adjoint of a matrix is given by the transpose of cofactor matrix.


Co-factor matrix of B =


adj(B) =


(A’)-1 =


Hence,


(A’)-1 =


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