 Hello friends, welcome to the session, I am Madhga, let's discuss the question, find a joint of each of the matrices 1 and 2, our given matrix is 1, 2, 3, 4. Now, let's start with the solution, let A equal to matrix 1, 2, 3, 4, now since we have to find the adjoint of matrix A and we know that to find the adjoint of matrix, this is formed by the transpose of the matrix formed by the co-factors, so first of all we have to find the co-factors of the different elements of A, so co-factor of 1 that is A11 is denoted by A11 equal to minus 1 to the power 1 plus 1 into m11 where m11 is the minor of the first element, so this is given by minus 1 to the power 2 into m11 that is obtained by deleting the first row and first column, so we are left with 4, therefore m11 is 4, this is equal to co-factor of 1 is 4, now we will find the co-factor of 2 which is A12, A12 equal to minus 1 to the power 1 plus 2 into m12 that is the minor of the element 2 which is obtained by deleting the first row and second column, so we are left with 3, therefore A12 is equal to minus 1 to the power 3 into 3, so this is equal to minus 3, now we will find the co-factor of 3 that is A21 equal to A21 equal to minus 1 to the power 2 plus 1 into m21, so m21 here is obtained by deleting the second row and first column, so it is 2, therefore A21 is minus 1 to the power 3 into 2 which is equal to minus 2, now we will find the co-factor of 4 that is A22 equal to A22 equal to minus 1 to the power 2 plus 2 into m22, here we obtain minor by deleting the second row and second column that is 1, so we are left with 1 minus 1 to the power 4 into 1 which is equal to 1, therefore matrix formed by the co-factors minus 4 minus 3 minus 2 and 1, now we have to find the joint of A, therefore a joint of A is obtained by the transpose of the matrix formed by the co-factors that is 4 minus 3 minus 2 1 transpose, so this is equal to and we know that transpose of the matrix is obtained by interchanging its rows into column and column into rows, so we get 4 minus 3 minus 2 1, therefore we can say that a joint of matrix A equal to matrix 4 minus 2 minus 3 1, now hope you understood the solution and enjoy the session with me and take care.