If A= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ]_ 3 3 , then A⁻¹=

Step-by-step solution

The determinant of A = bmatrix 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 bmatrix evaluates to (A) = 3[(-3)(1) - (4)(-1)] + 3[(2)(1) - (4)(0)] + 4[(2)(-1) - (-3)(0)] = 3(1) + 3(2) + 4(-2) = 1 . The cofactor matrix is computed as C = bmatrix 1 & -2 & -2 -1 & 3 & 3 0 & -4 & -3 bmatrix , yielding the adjoint adj (A) = C^ = bmatrix 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 bmatrix . Thus, A⁻¹ = 1 (A) adj (A) = bmatrix 1 & -1 & 0 -2 & 3 & -4 -2 & 3 & -3 bmatrix . Computing A^2 = A A = bmatrix 3 & -4 & 4 0 & -1 & 0 -2 & 2 & -3 bmatrix an