How to Find Inverse of a Matrix

How to Find Inverse of a Matrix

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What is the inverse of Matrix?

Matrix's inverse is another matrix that gives the multiplicative identity when multiplied by the given Matrix. The inverse of a matrix A is A1 and A.A1 = A1.A = I (I is the identity matrix). An invertible matrix is one whose determinant is not zero and for which the inverse matrix can be calculated.

The Formula for the inverse of a Matrix

Consider A = [ab cd] as a 2×2 matrix. The formula gives the inverse Matrix of A.

A1 = 1|A| [db ca], |A| = ad  bc

As an example, the inverse of [12 34] is [21 3212] and we can see that:

A.A1 = [12 34] [21 3212] = [10 01]

A1.A = [21 3212] [12 34] = [10 01]

Free printable Worksheets

Exercises for Finding Inverse of a Matrix

1) Find the inverse of the matrix: A = [23 10]

2) Find the inverse of the matrix: A = [38 124]

3) Find the inverse of the matrix: A = [83 219]

4) Find the inverse of the matrix: A = [26 35]

5) Find the inverse of the matrix: A = [113 154]

6) Find the inverse of the matrix: A = [423 212]

7) Find the inverse of the matrix: A = [93 176]

8) Find the inverse of the matrix: A = [58 47]

9) Find the inverse of the matrix: A = [616 25]

10) Find the inverse of the matrix: A = [337 92]

 

1) Find the inverse of the matrix: A = [23 10]

|A| = 3
A1 = 13 [03 12] = [01 1323]

2) Find the inverse of the matrix: A = [38 124]

|A| = 84
A1 = 184 [48 123] = [121121 17128]

3) Find the inverse of the matrix: A = [83 219]

|A| = 9
A1 = 19 [93 218] = [113 7389]

4) Find the inverse of the matrix: A = [26 35]

|A| = 8
A1 = 18 [56 32] = [5834 3814]

5) Find the inverse of the matrix: A = [113 154]

|A| = 1
A1 = 11 [43 1511] = [43 1511]

6) Find the inverse of the matrix: A = [423 212]

|A| = 2
A1 = 12 [1223 24] = [6232 12]

7) Find the inverse of the matrix: A = [93 176]

|A| = 3
A3 = 13 [63 179] = [21 1733]

8) Find the inverse of the matrix: A = [58 47]

|A| = 3
A1 = 13 [78 45] = [7383 4373]

9) Find the inverse of the matrix: A = [616 25]

|A| = 2
A1 = 12 [516 26] = [528 13]

10) Find the inverse of the matrix: A = [337 92]

|A| = 3
A1 = 13 [27 933] = [2373 311]

Finding Inverse of a Matrix Practice Quiz