What is the Inverse of a Matrix?

The inverse of a matrix is a matrix evolved from the matrix, by multiplying which with that original matrix, an identity matrix is found. It's the quotient of the adjoint matrix of a given matrix and its determinant. An inverse matrix is found by the following steps:

1. A square matrix is selected and its invertibility is checked by finding its determinant. If det(Matrix)=0, then the matrix is called singular and is not invertible.
2. Then the cofactor matrix of the original matrix is determined.
3. Then the transpose of the cofactor matrix is found out, which is called adjoint or adjugate matrix of the original matrix.
4. The adjoint matrix is divided by the determinant of the original matrix which yields the inverse matrix.

Note that, only square matrices are invertible because only their determinants can be calculated.

About Inverse Matrix Calculator

The Inverse Matrix Calculator directly calculates the inverse of a given non-singular matrix. It is designed for students to make the task of finding inverse matrices easier.

Features:

The Inverse Matrix Calculator has the following features:

• Instantly calculates inverse of a matrix.
• Supports up to 4×4(4 columns and 4 rows) sized square matrix.
• Option to switch between decimals view and fractions view in the result.
• Clearing feature for recalculation after obtaining result.
• Reports error if any singular matrix is found.
• Modern UI and responsive mobile-friendly design.

Uses:

The Inverse Matrix Calculator has the following uses:

• Used to find the inverse of a given square matrix.
• Can be used to find linear algebraic expressions.

Try out our Matrix Determinant Calculator.