 Hello friends welcome to the session. I am Alga. We are going to discuss determinants I given question is find the inverse of each of the matrices if it exists given an exercises fire to 11 our sex exercises matrix minus 1 5 minus 3 2 now, let's start with the solution We are given a equal to matrix minus 1 5 minus 3 2 and since we have to find the a inverse which is equal to 1 upon determinant of a into a joint of a As you know that a inverse is possible only if Determinant of a is not equal to 0. So first of all we'll find the determinant of a which is determinant of a equal to minus 2 and Plus 13 or 15 Which is equal to 13 not equal to 0 there this implies a Is a Non-singular matrix This implies a inverse exist Now we'll find the co-factors for calculating the adjoint of a co-factor of minus 1 equal to minus 1 to the power 1 plus 1 into 2 Which is equal to 2 now co-factor of 5 equal to minus 1 to the power 1 plus 2 in 2 minus 3 Which is equal to 3? Similarly, we'll write the co-factors of minus 3 and 2 Co-factor of minus 3 equal to minus 5 and co-factor of 2 equal to minus 1 therefore the matrix obtained by the co-factors is Matrix 2 3 minus 5 minus 1 now we'll find the adjoint of a therefore adjoint of a Equal to transpose of matrix formed by the co-factors, which is 2 3 minus 5 minus 1 transpose this is equal to 2 3 minus 5 minus 1 Now we'll find the a inverse a inverse equal to 1 upon determinant of a into adjoint of a which is equal to 1 upon 13 into adjoint of a is 2 minus 5 3 and minus 1 so a Inverse equal to 1 upon 13 into matrix 2 minus 5 3 1 which is a required answer Hope you understood the solution and enjoyed the session. Goodbye and take care