 Hello friends welcome to the session. I am Malka. We are going to discuss matrices now if fx equal to Matrix cos x minus sine x 0 sine x cos x 0 001 then we have to show that fx into f y equal to f of x plus y Now let's start with the solution We are given that fx equal to matrix cos x minus sine x 0 sine x cos x 0 001 Now we can calculate the find the value of f y therefore f y equal to Matrix cos y minus sine y 0 sine y cos y 0 001 Now we will consider the LHS of our given question that is fx into f y fx into f y that is matrix cos x minus sine x 0 sine x cos x 0 001 into matrix cos y minus sine y 0 sine y cos y 0 0 0 1 On multiplying these two we get cos x cos y plus minus of sine x into sine y Plus 0 into 0 on multiplying the given matrices We get the required matrix now this can also be written as cos x Cos y minus sine x sine y Then minus cos x sine y Minus sine x cos y and this is 0 then sine x cos y plus cos x sine y Minus sine x sine y Plus cos x cos y then again 0 then 0 0 and 1 On using the identity cos x cos y minus sine x sine y equal to cos x plus y and Sine x cos y plus cos x sine y equal to sine x plus y the above matrix can be written as cos x plus y Then minus Sine x plus y 0 then again sine x plus y cos x plus y 0 0 0 1 So this is our LHS now we'll see RHS RHS is f of x plus y which can be written as Matrix cos x plus y minus sine x plus y is 0 sine x plus y cos x plus y is 0 and 0 0 1 this is our RHS now on comparing LHS and RHS we find that LHS is equal to RHS So this is proof. Hope you understood the solution and enjoyed the session. Goodbye and take care