Question -
Answer -
(i) The criteria of existence of inverse matrix is thedeterminant of a given matrix should not equal to zero.
Now, |A| = cos θ (cos θ) +sin θ (sin θ)
= 1
Hence, A – 1 exists.
Cofactors of A are
C11 = cos θ
C12 = sin θ
C21 = – sin θ
C22 = cos θ
(ii) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
Now, |A| = – 1 ≠ 0
Hence, A – 1 exists.
Cofactors of A are
C11 = 0
C12 = – 1
C21 = – 1
C22 = 0
(iii) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
(iv) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
Now, |A| = 2 + 15 = 17 ≠ 0
Hence, A – 1 exists.
Cofactors of A are
C11 = 1
C12 = 3
C21 = – 5
C22 = 2
