 Hello and welcome to the session. Let us discuss the following question which says evaluate the determinant of order 2 whose elements are a plus iota b, c plus iota d minus c plus iota d and a minus iota b. Before moving on to the solution let us recall an identity that is x plus y into x minus y is equal to x square minus y square also iota square is equal to minus 1. So this is the key idea for this question. Now let us proceed with its solution. We need to evaluate the determinant of order 2 with elements a plus iota b, c plus iota d minus c plus iota d and a minus iota b. We can also write it as the determinant of order 2 with elements a plus iota b, c plus iota d. Let us take minus common from this so we get minus of c minus iota d and last element is a minus iota b. So this will be equal to a plus iota b into a minus iota b minus c plus iota d into minus of c minus iota d. Now we know that x plus y into x minus y is equal to x square minus y square. So here a plus iota b into a minus iota b will be a square minus iota b square plus now c plus iota d into c minus iota d will be c square minus iota d square which will be equal to a square minus iota square b square plus c square minus iota square b square. Now iota square is equal to minus 1 so this will be equal to a square plus b square plus c square plus d square. Thus the given determinant is equal to a square plus b square plus c square plus d square. With this we finish this session hope you must have enjoyed it. Goodbye take care and keep smiling.