 Hello friends, welcome to the session. I'm Malka. We are going to discuss matrices if a equal to matrix 3 minus 2 4 minus 2 and I That is identity matrix, which is equal to 1 0 0 1 We have to find k so that a square equal to k a minus 2 I now let's start with the solution We are given a equal to matrix 3 minus 2 4 minus 2 We have to calculate a square that is a into a which can be written as Matrix 3 minus 2 4 minus 2 multiply by matrix 3 minus 2 4 minus 2 which is equal to 3 into 3 plus minus 2 into 4 3 into minus 2 Plus minus 2 into minus 2 and for second row 4 into 3 plus minus 2 into 4 4 into minus 2 Plus minus 2 into minus 2 This gives a square equal to 9 minus 8 minus 6 plus 4 12 minus 8 minus 8 plus 4 Therefore a square equal to 1 minus 2 4 and minus 4 Now we'll calculate the value of k a K a equal to k into matrix a which is 3 minus 2 4 minus 2 this is equal to 3 k minus 2 k 4 k and minus 2 k Now we'll calculate the value of minus 2 I therefore minus 2 I Equal to minus 2 into identity matrix, which is 1 0 0 1 This implies minus 2 I equal to minus 2 0 0 minus 2 Now we'll calculate the value of k a minus 2 I Therefore k a minus 2 I equal to 3 k minus 2 k 4 k minus 2 k Plus 2 I which is minus 2 0 0 minus 2 This is equal to 3 k minus 2 minus 2 k plus 0 4 k plus 0 minus 2 k minus 2 According to question a square equal to k a minus 2 I this implies Value of a square is matrix 1 minus 2 4 minus 4 and value of k a minus 2 I is matrix 3 k minus 2 minus 2 k 4 k minus 2 k minus 2 Now on equating the corresponding elements we get Hence k equal to 1 is the answer. Hope you understood the solution and enjoyed the session. Goodbye and take care