# Inverse of a Matrix

**How to find Inverse of a Matrix?**

To find inverse of a matrix, first we must check whether the matrix is singular or invertible. Here we find inverse of a 2 x 2 matrix.

# Singular OR Invertible Matrix

Consider a Matrix If*ad - bc =*0, then the matrix is said to be a Singular Matrix.

If

*ad - bc*0, then the matrix is said to be an Invertible Matrix.

The inverse of a matrix only exists if the matrix is invertible.

# Theorem

Consider a matrix If the matrix is invertible, then its inverse is,# Practice Problems

**Show that**

*Example 1.**A*is an invertible matrix and find inverse, when

*Solution:*First check whether the matrix is invertible or not

*ad - bc =* (2)(4) - (2)(-3) = 8 + 6 = 14 0

**Find inverse of the matrix**

*Example 2.*

*Solution:*First check whether the matrix is invertible or not

*ad - bc =* (4)(-5) - (2)(-10) = -20 + 20 = 0

**Consider question No.3 of GRE Mathematics (GR9768)**

**If is invertible under matrix multiplication, then its inverse is?**

*Example 3.*

*Solution:*Recall the definition (theorem) of inverse of a matrix

If is invertible, then So the inverse of the given matrix is,