 Hello friends, welcome to the session. I am Alga. We are going to discuss matrices. We are given that we have to show that matrix 1, 2, 3, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 3, 4 is not equal to the product of matrix minus 1, 1, 0, 0, minus 1, 1, 0, 3, 4 into matrix 1, 2, 3, 0, 1, 0, 1, 1, 0. Now let's start with the solution. In the given question, we have to show that LHS is not equal to RHS. So let's start with LHS. We are given that 1, 2, 3, 0, 1, 0, 1, 1, 0 is multiplied by matrix minus 1, 1, 0, 0, minus 1, 1, 2, 3, 4. So this is equal to 1 into minus 1 plus 2 into 0 plus 3 into 2, then 1 into 1 plus 2 into minus 1 plus 3 into 3, 1 into 0 plus 2 into 1 plus 3 into 4. Similarly, 0 into minus 1 plus 1 into 0 plus 0 into 2, then 0 into 1 plus 1 into minus 1 plus 0 into 3, 0 into 0 plus 1 into 1 plus 0 into 4. Similarly, for the third row 1 into minus 1 plus 1 into 0 plus 0 into 2, 1 into 1 plus 1 into minus 1 plus 0 into 3, 1 into 0 plus 1 into 1 plus 0 into 4. So this is equal to minus 1 plus 0 plus 6, 1 minus 2 plus 9, 0 plus 2 plus 12, 0 plus 0 plus 0, 0 minus 1 plus 0, 0 plus 1 plus 0, minus 1 plus 0 plus 0, 1 minus 1 plus 0, 0 plus 1 plus 0. So this is equal to 5, 8, 14, 0, minus 1, 1, minus 1, 0 and 1. So this is our LHS. Now we will go for RHS. We will multiply the given matrices, which is minus 1, 1, 0, 0, minus 1, 1, 2, 3, 4, multiply by matrix 1, 2, 3, 0, 1, 0, 1, 1, 0. So this is equal to minus 1 into 1 plus 1 into 0 plus 0 into 1, then minus 1 into 2 plus 1 into 1 plus 0 into 1 minus 1 into 3 plus 1 into 0 plus 0 into 0. Then 0 into 1 minus 1 into 0 plus 1 into 1, 0 into 2 minus 1 into 1, then plus 1 into 1, 0 into 3 minus 1 into 0 plus 1 into 0. And then for the last row, 2 into 1 plus 3 into 0 plus 4 into 1, 2 into 2 plus 3 into 1 plus 4 into 1, then 2 into 3 plus 3 into 0 plus 4 into 0. This can be written as minus 1 plus 0 plus 0 minus 2 plus 1 plus 0 minus 3 plus 0 plus 0, 0 plus 0 plus 1, 0 minus 1 plus 1, 0 minus 0 plus 0, 2 plus 0 plus 4, 4 plus 3 plus 4, 6 plus 0 plus 0. This is equal to matrix minus 1, minus 1, minus 3, 1, 0, 0, 6, 11 and 6. So this is our RHS. Now, here we see that LHS is not equal to RHS, hence the product of the matrix 1, 2, 3, 0, 1, 0, 1, 1, 0, minus 1, 1, 0, 0 minus 1, 1, 2, 3, 4 is not equal to RHS. Minus 1, 1, 0, 0 minus 1, 1, 2, 3, 4 into matrix 1, 2, 3, 0, 1, 0, 1, 1, 0. So this is proved. Hope you understood the solution and enjoyed the session. Goodbye and take care.