 Hello friends and how are you all doing today? The question says if a is equal to matrix having elements as 3, 4, minus 2, minus 2, find k such that a square is equal to k into a minus 2i square. Let us start with our solution. Here we are given the matrix A as this. Let us first find out a square. It is 3, 4, minus 2, minus 2 into 3, 4, minus 2, minus 2. On solving it we have the value of a square as in the first row 9 minus 8 minus 6 plus 4 in the second row 12 minus 8 minus 8 plus 4 giving us the answer of a square as 1 minus 2 4 minus 4. Now we need to prove that a square is equal. Sorry we need to find the value of k such that a square is equal to k into a minus 2i square. So let us substitute the values that we have above. We have a square as 1 minus 2 4 minus 4 equal to k into a that is 3 minus 2 4 minus 2 minus 2 i square that will be 1, 0, 0, 1 always. Further we have 1 minus 2 4 minus 4 matrix equal to now let us solve it we have 3k minus 2 minus 2k is minus 0. In the second row we have 4k minus 0 minus 2k minus 2. Now on comparing both sides we have minus 3k minus 2 equal to 1 and minus 2k minus 0 is equal to minus 2. And 4k minus 0 is equal to 4 minus 2k minus 2 is equal to minus 4. All this implies that the value of k is equal to 1 in each and every case. So the answer to this question is that the value of k is equal to 1. So this completes the solution hope you understood it have a nice day. Thank you.