 Hello friends welcome to the session. I am Malka. We are going to discuss determinants A given question is find the inverse of each of the matrices if it exists given in exercises 5 to 11 5th exercises Matrix 2 minus 2 4 3 now. Let's start with the solution We are given that a equal to matrix 2 minus 2 4 3 now. Let me tell you the basic idea behind the question is There are two type of matrixes Singular matrix and non-singular matrix Singular matrix is a square matrix a is said to be singular if determinant of a equal to 0 and Non-singular matrix is a square matrix a is said to be non-singular if Determinant of a is not equal to 0 now a Square matrix is invertible if and only if a which is a square matrix is Non-singular matrix that is determinant of a is not equal to 0 now Let a be a non-singular square matrix then a inverse equal to 1 upon determinant of a into a joint of a As we have seen that a inverse equal to 1 upon determinant of a into a joint of a and we already know How to calculate a joint of a Which is transpose of a so let let us first find out the determinant of a determinant of a equal to 3 into 6 Minus and minus of 8 becomes plus 8. This is equal to 14 which is not equal to 0 this shows that since determinant of a is not equal to 0 Therefore a inverse exist Now we'll calculate the co-factors of matrix a Co-factor of 2 equal to minus 1 to the power 1 plus 1 into 3 Which is equal to 3 similarly co-factor of Minus 2 equal to minus 1 1 plus 2 into 4 Which is equal to minus 4 now we write the co-factor of 4 and 3 Co-factor of 4 equal to 2 co-factor of 3 equal to 2 Therefore the matrix obtain by the co-factors is Now the matrix formed by the co-factors equal to matrix 3 minus 4 to 2 Now we'll find the adjoint of a therefore Adjoint of a which is transpose of the matrix formed by the co-factors That is 3 minus 4 to 2 transpose which is equal to 3 minus 4 to 2 Now we'll find the a inverse therefore a inverse equal to 1 upon determinant of a Into adjoint of a as we have already calculated the determinant of a therefore a inverse equal to 1 upon 14 into adjoint of a which is 3 2 minus 4 to which is a required answer Hope you understood the solution and enjoyed the session goodbye and take care