Question

Find the inverse of the matrices and verify that A-1A = I3.

(\begin{bmatrix} 1 & 3 & 3\[0.3em] 1&4 & 3 \ 1 & 3& 4\end{bmatrix})

Answer 1

|A| =

= 1(16 – 9) – 3(4 – 3) + 3(3 – 4)

= 7 – 3 – 3

= 1

So A – 1 exists

Co-factors of A are

C11 = 7

C21 = – 3

C31 = – 3

C12 = – 1

C22 = – 1

C32 = 0

C13 = – 1

C23 = 0

C33 = 1

As we know

A-1A = I3

Hence proved.