Using elementary transformations, find the inverse of each of the matrices.

First of all we need to check whether the matrix is invertible or not. For that-

For the inverse of a matrix A to exist,

Determinant of A ≠ 0

Here ∣A∣ = (2)(3) – (1)(5) = 1

So the matrix is invertible.

Now to find the inverse of the matrix,

We know AA^-1 = I

Let’s make augmented matrix-

→ [ A : I ]

→

Apply row operation- R₂→ R₂ – R₁

→

Apply row operation- R₁→ R₁/2

→

Apply row operation- R₁→ R₁ - 5R₂

→

Apply row operation- R₂→ 2R₂

→

The matrix so obtained is of the form –

→ [ I : A^-1 ]

Hence inverse of the given matrix-

→