 Hi and welcome to our session. Let us discuss the following question. The question says if a is equal to 2 by 2 matrix whose elements are 2, 3, 1, 2, then prove that a cube minus 4a square plus a is equal to 0. We begin with the solution. We are given that a is equal to 2 by 2 matrix whose elements are 2, 3, 1, 2. Now let's first find out a square. Now a square is equal to a into a and this is equal to this matrix multiplied by itself. Multiply elements of first row with these two columns of this matrix. So we have 2 into 2 plus 3 into 1 and then 2 into 3 plus 3 into 2. And now we will multiply the second row of this matrix with these two columns of this matrix. So now we have 1 into 2 plus 2 into 1, 1 into 3 plus 2 into 2. Now this is equal to 2 by 2 matrix whose elements are 4 plus 3, 6 plus 6 is equal to 2 by 2 matrix whose elements are that a square is equal to 2 by 2 matrix whose elements are 7, 12, 14, 7 into a square matrix in which elements are, in which elements are equal to 2 by 2 matrix 21, 7 is equal to 2 by 2 matrix in which elements are 2, 0. So let's now consider matrices as we get the new matrix in which elements are 2, 45. These two matrices we get new matrix in which elements are 28, 48, minus 48, 16, minus 16, 28, minus 28 equal to a 2 by 2 matrix in which elements are 0, 0, 0, 0 and this is equal to 0 matrix. Hence we have proved that left inside is equal to right hand. So this completes the session. Bye and take care.