Question

If A = \(\begin{bmatrix}1&3&3\\[0.3em]1&4&3\\[0.3em]1&3&4\end{bmatrix}\)then find A^-1 and show that A^-1.A= I₃.

Answer 1

= 1(16 – 9) – 3(4 – 3) + 3(3 – 4)

= 7 – 3 – 3

|A|= 1 ≠ 0

So, A^-1 exists.

On finding adjoint of A,

Matrix formed by adjoint of A,

Again to prove that

Hence, A^-1A = I₃.