If A = 1 2 bmatrix -1 & - 3 3 & -1 bmatrix then A⁻¹ - A^2 is not

Step-by-step solution

Given A = 1 2 bmatrix -1 & - 3 3 & -1 bmatrix Calculating A^2 : A^2 = 1 4 bmatrix -1 & - 3 3 & -1 bmatrix bmatrix -1 & - 3 3 & -1 bmatrix = 1 4 bmatrix 1-3 & 3 + 3 - 3 - 3 & -3+1 bmatrix = 1 4 bmatrix -2 & 2 3 -2 3 & -2 bmatrix = 1 2 bmatrix -1 & 3 - 3 & -1 bmatrix Now, finding the determinant of A : |A| = ( 1 2 )^2 ((-1)(-1) - (- 3 )( 3 )) = 1 4 (1 + 3) = 1 The inverse of A is given by A⁻¹ = 1 |A| adj (A) : A⁻¹ = 1 2 bmatrix -1 & 3 - 3 & -1 bmatrix Thus, A⁻¹ - A^2 = 1 2 bmatrix -1 & 3 - 3 & -1 bmatrix - 1 2 bmatri