Frequently Asked Questions on Inverse of Matrix

What is Inverse of Matrix?

Reciprocal of a matrix is called the Inverse of a matrix. Only square matrices with non-zero determinants are invertible. Suppose for any square matrix A with inverse matrix B their product is always an identity matrix (I) of the same order.

[A]×[B] = [I]

What is Matrix?

Matrix is a rectangular array of numbers that are divided into a defined number of rows and columns. The number of rows and columns in a matrix is referred to as its dimension or order.

What is the Inverse of 2×2 Matrix?

For any matrix A or order 3×3 its inverse is found using the formula,

A^-1 = (1 / |A|) × Adj A

What is the Inverse of 3×3 Matrix?

The inverse of any square 3×3 matrix (say A) is the matrix of the same order denoted by A^-1 such that their product is an Identity matrix of order 3×3.

[A]_3×3 × [A^-1]_3×3 = [I]_3×3

Are Adjoint and Inverse of Matrix the same?

No, the adjoint of a matrix and the inverse of a matrix are not the same. 

How to use the Inverse of Matrix?

The inverse of a matrix is used for solving algebraic expressions in matrix form. For example, to solve AX = B, where A is the coefficient matrix, X is the variable matrix and B is the constant matrix. Here the variable matrix is found using the inverse operation as,

X = A^-1B

What are Invertible Matrices?

The matrices whose inverse exist are called invertible. Invertible matrices are matrices that have a non-zero determinant.

Why does Inverse of 2 × 3 Matrix not exist?

The inverse of only a square matrix exists. As the 2 × 3 matrix is not a square matrix but rather a rectangular matrix thus, its inverse does not exist.

Similarly, the 2 × 1 matrix is also not a square matrix but rather a rectangular matrix thus, its inverse does not exist.

What is Inverse of Identity Matrix?

The inverse of an identity matrix is the identity matrix itself. This is because the identity matrix, denoted as I (or I_n for an n ×n matrix), is the only matrix for which every element along the main diagonal is 1 and all other elements are 0. When we multiply an identity matrix by itself (or its inverse), we get the identity matrix again.

The inverse of Matrix is the matrix that on multiplying with the original matrix results in an identity matrix. For any matrix A, its inverse is denoted as A^-1.

Let’s learn about the Matrix Inverse in detail, including its definition, formula, methods on how to find the inverse of a matrix, and examples.