 Hello and welcome to the session. If a is equal to 1, 2, 4, 2, then show that mod of 2a is equal to 4 into determinant a. Now, let us write the solution before this. Let us see how to find out the determinant. Determinant of a is denoted by mod of a or determinant a or delta. Consider a system of linear equations a1x plus b1y is equal to c1 and a2x plus b2y is equal to c2 which is associated with the square matrix a which is equal to a1b1 a2b2 thus determinant a is equal to mod of a is equal to a1b2 minus a2b1. Now, let us write the solution. Given to us as a is equal to 1, 2, 4, 2 which implies 2a is equal to 2, 4, 8, 4 therefore determinant of 2a is equal to 2, 4, 8, 4 which is equal to 8 minus 32 which is equal to minus 24. Now, mod of 8 that is determinant of a is equal to 1, 2, 4, 2 no solving this we get 2 minus 8 which is equal to minus 6 therefore 4 into determinant a is equal to 4 multiplied by minus 6 which is equal to minus 24 hence mod of 2a is equal to 4 into mod of a that is determinant of 2a is equal to 4 into determinant of a hence proved. I hope you understood this session. Bye and have a nice day.