 Hi and welcome to the session. I am Deepika here. Let's discuss a question. If A is equal to matrix whose elements are 2 minus 3, 5, 3, 2 minus 4, 1, 1 minus 2, find A inverse using A inverse. So all the system of equations 2x minus 3y plus 5z is equal to 11, 3x plus 2y minus 4z is equal to minus 5, x plus y minus 2z is equal to minus c. So let's start the solution of equations. x is equal to b is equal to e1 minus 3, 2, 1, 5 minus 4 minus 2. So A is this matrix. x is equal to rxyz 2 minus 2 that is minus 4, 2 into minus 4 plus 4 and this is minus of minus 3 into x plus 4 minus 2. This is equal to 0 minus 2 that is minus 6 plus 5 into 1 that is 5. So this is equal to minus 1 which is not equal to 0. So this implies is non-singular and so its inverse exists of each and every element of A. So co-factor of 2 is equal to this is equal to minus 1 raised to power 1 plus 1 into minus 6 plus 4, 1 raised to power 1 plus 1 into 2 into minus 2 that is minus 4 plus 4. So this is equal to 0 is equal to minus 1 raised to power 1 plus 2 into minus 6, find out the co-factors of each and every element which are as follows. The matrix formed by the co-factors is by the co-factors this is 0, 2, 1, minus 1, minus 9, minus 5, 2, 23 and 13. Therefore a joint A is equal to of this matrix that is minus 1, minus 9, minus 5, 2, 23 up to find A inverse and therefore A inverse is equal to 1 over determinant A into adjoint A. So this is equal to determinant A is or minus 1. So A inverse is equal to 0, minus 2, minus 1, 1, minus 2, minus 23, minus 13. This is our A inverse. Equal to A inverse B is this matrix minus 2, minus 1, 1, 9, 5, minus 2, minus 23, minus 13 into B. B's are 11, minus 5, minus 3. So this is equal to 1 into minus 5, minus 5, plus 6. Again minus 2 into 11 this is minus 22, minus 45, plus 69 and here it is minus 11, minus 25, plus 39. This is equal to this implies that it is equal to 1, 2, 3. So by equating coefficients of corresponding elements we get x is equal to y is equal to and z is equal to 3, minus 2, minus 1, 1, minus 2, minus 23 and minus 13 equal to 1, y is equal to 2 and z is equal to 3. So this is the answer for the above question. I hope the question is clear to you. Bye and have a nice day.