 Hello friends, welcome to the session. I am Malka. 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 9 exercises, matrix 2, 1, 3, 4, minus 1, 0, minus 7, 2, 1. Now let's start with the solution. We are given A equal to matrix 2, 1, 3, 4, minus 1, 0, minus 7, 2, 1. Now we'll find the determinant of A. Therefore, determinant of A equal to 2 into minus 1, 0, 2, 1, minus 1 into determinant 4, 0, minus 7, 1, plus 3 into determinant 4, minus 1, minus 7, 2. This is equal to 2 into minus 1, minus 0, minus 1 into 4, plus 0, plus 3, 8, minus 7. This is equal to minus 2, minus 4, plus 3. This is equal to minus 3. This implies that determinant of A not equal to 0, this implies A inverse exists. Now we will find the co-factor of the elements. Co-factor of 2 equal to minus 1 to the power 1 plus 1 into minus 1, minus 0, equal to minus 1. Co-factor of 1 equal to minus 1, 1 plus 2 into 4, plus 0, which is equal to minus 4. Similarly, we'll write the co-factor of other elements. Co-factor of 3 equal to 1, co-factor of 4 equal to 5, co-factor of minus 1 equal to 23, co-factor of 0 equal to minus 11, co-factor of minus 7 equal to 3, co-factor of 2 equal to 12, co-factor of 1 equal to minus 6. Therefore, the matrix form by the co-factors is equal to matrix minus 1, minus 4, 1, 5, 23, minus 11, 3, 12, minus 6. Now we'll find the value of a joint of A, which is equal to transpose of the matrix form by the co-factor that is minus 1, minus 4, 1, 5, 23, minus 11, 3, 12, minus 6. So, a joint of A equal to minus 1, minus 4, 1, 5, 23, minus 11, 3, 12, minus 6. Now we'll find the A inverse. A inverse equal to 1 upon determinant of A into a joint of A, which is equal to minus 1 upon 3 into matrix that is a joint of A, which is minus 1, 5, 3, minus 4, 23, 12, 1, minus 11, minus 6. Therefore, A inverse equal to minus 1 upon 3 into matrix minus 1, 5, 3, minus 4, 23, 12, 1, minus 11, minus 6, which is the required answer. Hope you understood the solution and enjoyed the session. Goodbye and take care.