 Hello everyone, how are you all today? The question says if A is equal to matrix having columns as 1, 2, 2, 1 elements in the column, fx is equal to x square minus 2x minus 3, show that f of A is equal to 0. Now here we have the matrix A as 1, 2, 2, 1 having its elements. And f of x is equal to x square minus 2x minus 3. So therefore we have f of A as A square minus 2A minus 3i, right? Now let us find out A square. It will be A into A that is equal to matrix A getting multiplied by matrix A. The answer comes out to be plus 2 and it will be 4 plus 1, which is equal to 5445. This is the value of A square. So therefore we have f of A equal to A square minus 2A minus 3i as value of A square that is substituted here minus 2A that is 1, 2, 2, 1 minus 3i that is 1, 0, 0, 1. Let us solve it. So we have 5445 minus 2442 minus 3003, right? Which is further equal to, on solving we have 5 minus 2 minus 3, 4 minus 4 minus 0, 4 minus 4 minus 0, 5 minus 2 minus 3 that is equal to 0, right? So hence we have shown that the value of f of A is equal to 0, right? So this completes the solution. Hope you understood it well and enjoyed it too. Have a nice day.