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How to Calculate the Inverse of a 2 x 2 Matrix.
MATRICES

How to Calculate the Inverse of a 2 x 2 Matrix.

Rosemary Njeri

The inverse of a matrix A is a matrix that, when multiplied by A results in the identity.

An identity matrix is a matrix equivalent to 1.

There is no concept of dividing by a matrix but, we can multiply by an inverse, which achieves the same thing.

Formula to calculate inverse matrix of a 2 by 2 matrix.

We begin by finding the determinant of the matrix.

Swap the positions of the elements in the leading diagonal.

And put a negative sign in front of the elements in the other diagonal.

Lastly, multiply the resultant matrix by 1 divided by the determinant.

Example:

Find the inverse of the following matrix.

Inverse of a 2 x 2 Matrix.

We begin by finding the determinant of the matrix.

Inverse of a 2 x 2 Matrix.

Therefore, the determinant of the matrix is -5.

Then we swap the positions of the elements in the leading diagonal and put a negative sign in front of the elements on the other diagonal.

Inverse of a 2 x 2 Matrix.

And lastly, multiply the resultant matrix by 1 divided by the determinant.

Inverse of a 2 x 2 Matrix.
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