If A= [ array ll 2 & 2 3 & 4 array ] , then A⁻¹ equals to

Step-by-step solution

Given the matrix A = bmatrix 2 & 2 3 & 4 bmatrix . The determinant of A is calculated as |A| = (2 4) - (2 3) = 8 - 6 = 2 . The inverse of a 2 2 matrix A = bmatrix a & b c & d bmatrix is given by A⁻¹ = 1 |A| bmatrix d & -b -c & a bmatrix . Substituting the values a=2, b=2, c=3, d=4 and |A|=2 , we get: A⁻¹ = 1 2 bmatrix 4 & -2 -3 & 2 bmatrix A⁻¹ = bmatrix 4 2 & -2 2 -3 2 & 2 2 bmatrix = bmatrix 2 & -1 -3/2 & 1 bmatrix . Answer: [ array cc 2 & -1 -3 / 2 & 1 array ]