 Hello friends, welcome to the session of Alka. Let's discuss the question. Find a joint of each of the matrices 1 and 2. Our given matrix is 1-1, 2, 2, 3, 5, minus 2, 0, 1. Now let's start with the solution. Let A equal to matrix 1-1, 2, 2, 3, 5, minus 2, 0, 1. Now we have to find the adjoint of the matrix A and we know that adjoint of any matrix A is the transpose of the matrix formed by the cofactors. So first of all let us form the cofactors. So cofactors of first element that is A11 that is 1 is equal to A11 equal to minus 1 to the power 1 plus 1 into m11. Now we all know that minor of 11 is obtained by deleting the first row and first column that is the determinant 3501. So this is equal to minus 1 to the power 2 into determinant of 3501. This is equal to minus 1 to the power 2 is 1 into 3 minus 0. Therefore cofactor of A11 is 3. Now let's see the cofactor of minus 1 which is denoted by A12. This is equal to minus 1 to the power 1 plus 2 into m12. Now minor of 12 is the determinant obtained by deleting the first row and second column. So this is equal to minus 1 to the power 3 into determinant that is 2, 5 minus 2, 1, 2, 5, minus 2, 1. So this is equal to minus 1 into 2 plus 10 equal to minus 12. Therefore the cofactor of minus 1 is minus 12. Similarly we will write the cofactor of other elements. Therefore cofactor of 2 equal to A13 is minus 1 to the power 1 plus 3 into 0 plus 6 which is equal to 6. Cofactor of 2 is A21 equal to minus 1 to the power 2 plus 1 into minus 1 minus 0 equal to 1. Cofactor of 3 equal to A22 equal to minus 1 to the power 2 plus 2 into 1 plus 2 equal to cofactor of 5 equal to A23 equal to minus 1 to the power 2 plus 3 into 0 minus 2. This is equal to 2 and cofactor of minus 2 equal to A31 equal to minus 1 to the power 3 plus 1 into minus 5 minus 6. So this is equal to minus 11. Now cofactor of 0 equal to A32 equal to minus 1 to the power 3 plus 2 into 5 minus 4 equal to minus 1. And cofactor of 1 equal to A33 equal to minus 1 to the power 3 plus 3 into 3 plus 2 equal to 5. So we have obtained all the cofactors now. Therefore matrix formed by the cofactors 11A12A13A21A22A23A31A32A33. So which is equal to 3 minus 12 6 1 5 2 minus 11 minus 1 and 5. Now we will find the adjoint of A and we all know that adjoint of A is obtained by the transport of the matrix formed by the cofactors. So 3 minus 12 6 1 5 2 minus 11 minus 1 5 transpose of the matrix formed by the cofactors. And we know that in the transpose of the matrix we interchange the rows into columns and column into rows. So this will be equal to 3 minus 12 6 1 5 2 minus 11 minus 1 5. Therefore we can say that adjoint of A equal to 3 1 minus 11 minus 12 5 minus 1 6 2 5 which is a required matrix. So hope you understood this solution and enjoyed the session. Goodbye and take care.