Answer :

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- R_{2}→ R_{2} – R_{1}

→

Apply row operation- R_{1}→ R_{1}/2

→

Apply row operation- R_{1}→ R_{1} - 5R_{2}

→

Apply row operation- R_{2}→ 2R_{2}

→

The matrix so obtained is of the form –

→ [ I : A^{-1} ]

Hence inverse of the given matrix-

→

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