# Find the inverse

Let the given matrix we have to find A-1.

Now A-1 will exist only of |A| ≠ 0

Let us first find |A| |A| = (-3) (-3) – (5)(2)

|A| = 9 – 10 = -1

Hence |A| ≠ 0 and A-1 exist

Now A-1 is given by Now adjoint(A) = CT where C is the cofactor matrix and CT is the transpose of cofactor matrix

The cofactor is given by

Cij = (-1) i+jMij …(a)

Where M represents minor

Mij is the determinant of matrix leaving the ith row and jth column

The cofactor matrix C will be Now transpose of C that is CT

For CT we will interchange the rows and columns Using (a) From matrix A the minors are

M11 = -3, M12 = 5, M21 = 2 and M22 = -3  Now inverse of A is   Now we have to solve the matrix equation  As we know that AA-1 = I hence multiply equation by A-1 from right side where I is identity matrix    Hence Rate this question :

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