 Hello friends welcome to the session I am Alka we are going to discuss determinants are given question is find the inverse of each Of the matrices if it exists given an exercises fire to element our eighth exercises matrix 100 3 3 0 5 2 minus 1 now. Let's start with a solution We are given a equal to matrix 1 0 0 3 3 0 5 2 minus 1 now. We'll find the determinant of a therefore determinant of a Equal to 1 into minus 3 and minus 0 Minus 0 plus 0 this is equal to minus 3 Therefore determinant of a is not equal to 0. This implies a inverse Exist now. We'll find the adjoint of a for which we have to find the cofactors cofactor of 1 equal to Minus 1 to the power 1 plus 1 in 2 Minus 3 Minus 0 this is equal to minus 3 now. We'll write the cofactor of other elements Cofactor of 0 is 3 cofactor of 0 is minus 9 cofactor of 3 equal to 0 cofactor of 3 equal to minus 1 Cofactor of 0 equal to minus 2 cofactor of 5 equal to 0 cofactor of 2 equal to 0 and cofactor of minus 1 equal to 3 Therefore matrix formed by the cofactor equal to matrix minus 3 3 minus 9 0 minus 1 minus 2 003 Now we'll find the adjoint of a therefore adjoint of a equal to Transpose of the matrix formed by the cofactors that is minus 3 3 minus 9 0 minus 1 minus 2 0 0 3 transpose This is equal to minus 3 3 minus 9 0 minus 1 minus 2 0 0 3 This is the value of adjoint of a now we'll find the a inverse Which is 1 upon determinant of a into a joint of a this is equal to minus 1 upon 3 into adjoint of a that is Matrix minus 3 0 0 3 minus 1 0 minus 9 minus 2 0 now therefore a inverse equal to a inverse equal to minus 1 upon 3 into matrix minus 3 0 0 3 minus 1 0 minus 9 minus 2 3 Which is the required answer? Hope you understood the solution and enjoyed the session. Goodbye and take care