 Hello friends, welcome to the session. I am Alka. We are going to discuss determinants. Our given question is, find the inverse of each of the matrices if it exists given in exercises 5 to 11 are 10 exercises matrix 1 minus 1 to 0 2 minus 3 3 minus 2 4. Now let's start with the solution. We are given that a equal to matrix 1 minus 1 to 0 2 minus 3 3 minus 2 4. Now we'll find the determinant of a therefore determinant of a equal to 1 into 8 minus 6 minus of minus 1 into 0 plus 9 plus 2 into 0 minus 6. This is equal to 2 plus 9 minus 12. This is equal to minus 1 which is not equal to 0. This implies a inverse exists. Now we will find the co-factors of the elements. Co-factor of 1 equal to minus 1 to the power 1 plus 1 into 8 minus 6 that is equal to 2. Co-factor of minus 1 equal to minus 1 to the power 1 plus 2 into 0 plus 9 which is equal to minus 9. Similarly, we'll write the co-factor of other elements. Co-factor of 2 equal to minus 6. Co-factor of 0 equal to 0. Co-factor of 2 equal to minus 2. Co-factor of minus 3 equal to minus 1. Co-factor of minus 2 equal to 3. Co-factor of 4 equal to 2. Therefore, matrix formed by the co-factor equal to matrix 2 minus 9 minus 6 0 minus 2 minus 1 minus 1 3 2. Now we'll find the adjoint of a therefore adjoint of a equal to transpose of the matrix formed by the co-factors. This is equal to 2 minus 9 minus 6 0 minus 2 minus 1 minus 1 3 2. So this is the value of adjoint of a therefore a inverse equal to 1 upon determinant of a into adjoint of a which is equal to minus 1 upon 1 into matrix 2 minus 9 minus 6 0 minus 2 minus 1 minus 1 3 2. Therefore, a inverse equal to matrix minus 2 0 1 9 2 minus 3 6 1 minus 2 which is a required answer. Hope you understood the solution and enjoyed the session. Goodbye and take care.