Question

Find the inverse of the following matrices.

(\begin{bmatrix} 1 & 0& 0 \[0.3em] 0&cos α&sin α\[0.3em] 0 &sin α&-cos α\end{bmatrix})

Answer 1

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

|A| =

= – (cos2 α – sin2 α)

= – 1

So, A – 1 exists

Co-factors of A are

C11 = – 1

C21 = 0

C31 = 0

C12 = 0

C22 = – cos α

C32 = – sin α

C13 = 0

C23 = – sin α

C33 = cos α