Which of the following matrices are invertible or singular F

Which of the following matrices are invertible or singular? Find the inverse of those that are invertible.

a)

b)

c)

d)

NOTE: These are matrices. I did not know how to get the bracket so I but the entries in a table. Part a is 2x2 b) is 2x2 c) is 3 x3 and d) is 3x3

Solution

step 1:
find determinant of matrix
If determinant = 0, matrix is singular.Inverse will not exist
If determinant !=0, inverse exist

a)
det of
-2 2/3
1 -1/2

= (-2)*(-1/2) - (1)*2/3
= 1 - 2/3
=1/3
which is non zero. Hence invese exist
Inverse is
=1/det * -1/2 -2/3
-1 -2
= -1/6 -2/9
-1/3 -2/3

b)
det of
1 -2
3 6
= 1*6 - (-2)*3
= 12

inverse =
1/12 * 6 2
-3 1
= 1/2 1/6
-1/4 1/12

Please do rest by yourself. I am allowed to answer only 1 question at a time