Question

Find the inverse of each of the following matrices:

(i) \(\begin{bmatrix} a & b\\[0.3em] c&\frac{1 + bc}{a}\end{bmatrix}\)

(ii) \(\begin{bmatrix} 2 & 5\\[0.3em] -3&1\end{bmatrix}\)

Answer 1

(i) Criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

(ii) Criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 2 + 15 = 17

So, A ^{– 1} exists.

Co-factors of A are

C₁₁ = 1

C₁₂ = 3

C₂₁ = – 5

C₂₂ = 2