 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says if A is the matrix whose elements are 2 minus 3, 3, 4 show that A squared minus 6A plus 17i is equal to 0, hence find A inverse. So let's start the solution. Now the elements of matrix A are given to us. So we have A squared is equal to A into A which is further equal to matrix A into matrix A. Now we know that to get the elements of this product matrix we will take the rows of this first matrix and the columns of the second matrix and then we will multiply them element wise and we will take this up. So the elements of the product matrix are 2 into 2 plus minus 3 into 3 which is minus 5, 2 into minus 3 plus minus 3 into 4 which is minus 18, 3 into 2 plus 4 into 3 which is 18, 3 into minus 3 plus 4 into 4 which is 7. So A squared is the matrix whose elements are minus 5, minus 18, 18, 7. Now A squared minus 6A plus 17i is equal to matrix whose elements are minus 5, minus 18, 18, 7, minus 6 into matrix A whose elements are 2 minus 3, 3, 4 plus 17 into identity matrix. So the elements of I are 1, 0, 0, 1. Now this is again equal to matrix whose elements are minus 5, minus 18, 18, 7 plus matrix whose elements are minus 6 into 2 minus 12, minus 6 into minus 3, 18, minus 6 into 3, minus 18, minus 6 into 4, minus 24 plus matrix whose elements are 17, 0, 0, 17. Now we will add these 3 matrices. So this is equal to matrix whose elements are minus 5, minus 12 plus 17, minus 18, plus 18, plus 0, 18, minus 18, plus 0, 7, minus 24, plus 17. Now this is further equal to 0 matrix and this is equal to 0. Therefore A squared minus 6A plus 17i is equal to 0. Let us give this as number 1. Now we will find A inverse. So on pre-multiplying equation 1 by A inverse we get A inverse into A square minus 6A inverse A plus 17A inverse I is equal to 0 or this can be written as now A inverse into A square is equal to A minus 6 into A inverse A which is I plus 17 into A inverse I which is A inverse is equal to 0 or we have A inverse is equal to 1 over 17 into matrix 6I minus A and this is equal to 1 over 17 into matrix 6I minus A. Now 6I is the matrix whose elements are 6, 0, 0, 6 minus A is the given matrix whose elements are 2 minus 3, 3, 4 and this is further equal to 1 over 17 into matrix whose elements are 6 minus 2 that is 4, 0 plus 3 which is minus 3, 6 minus 4 which is 2. So we have A inverse is equal to 1 over 17 into matrix whose elements are 4, 3 minus 3, 2. So this is the answer for the above question. This completes our session. I hope the solution is clear to you. Bye and have a nice day.