Question -
Answer -
(i) The criteria of existence of inverse matrix is thedeterminant of a given matrix should not equal to zero.
|A| = 
= 1(6 – 1) – 2(4 – 3) + 3(2 – 9)
= 5 – 2 – 21
= – 18≠ 0
Hence, A – 1 exists
Cofactors of A are
C11 = 5
C21 = – 1
C31 = – 7
C12 = – 1
C22 = – 7
C32 = 5
C13 = – 7
C23 = 5
C33 = – 1
(ii) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
|A| = 
= 1 (1 + 3) – 2 (– 1 + 2) + 5 (3 + 2)
= 4 – 2 + 25
= 27≠ 0
Hence, A – 1 exists
Cofactors of A are
C11 = 4
C21 = 17
C31 = 3
C12 = – 1
C22 = – 11
C32 = 6
C13 = 5
C23 = 1
C33 = – 3
(iii) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
|A| = 
= 2(4 – 1) + 1(– 2 + 1) + 1(1 – 2)
= 6 – 2
= – 4≠ 0
Hence, A – 1 exists
Cofactors of A are
C11 = 3
C21 = 1
C31 = – 1
C12 = + 1
C22 = 3
C32 = 1
C13 = – 1
C23 = 1
C33 = 3
(iv) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
|A| = 
= 2(3 – 0) – 0 – 1(5)
= 6 – 5
= 1≠ 0
Hence, A – 1 exists
Cofactors of A are
C11 = 3
C21 = – 1
C31 = 1
C12 = – 15
C22 = 6
C32 = – 5
C13 = 5
C23 = – 2
C33 = 2
(v) The criteria of existence of inverse matrix is thedeterminant of a given matrix should not equal to zero.
|A| = 
= 0 – 1 (16 – 12) – 1 (– 12 + 9)
= – 4 + 3
= – 1≠ 0
Hence, A – 1 exists
Cofactors of A are
C11 = 0
C21 = – 1
C31 = 1
C12 = – 4
C22 = 3
C32 = – 4
C13 = – 3
C23 = 3
C33 = – 4
(vi) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
|A| = 
= 0 – 0 – 1(– 12 + 8)
= 4≠ 0
Hence, A – 1 exists
Cofactors of A are
C11 = – 8
C21 = 4
C31 = 4
C12 = 11
C22 = – 2
C32 = – 3
C13 = – 4
C23 = 0
C33 = 0
(vii) The criteria of existence of inverse matrix isthe determinant of a given matrix should not equal to zero.
|A| = 
– 0 + 0
= – (cos2 α – sin2 α)
= – 1≠ 0
Hence, A – 1 exists
Cofactors 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
