If A = bmatrix 3 & 2 & 6 1 & 1 & 2 2 & 2 & 5 bmatrix , B = bmatrix 1 0 1 bmatrix such that XA = B^T and A⁻¹Y = B , then XY =

Step-by-step solution

Given XA = B^T Post-multiplying by A⁻¹ , we get X = B^T A⁻¹ Given A⁻¹Y = B Pre-multiplying by A , we get Y = AB Now, XY = (B^T A⁻¹)(AB) Using the associative property of matrix multiplication, XY = B^T (A⁻¹A) B XY = B^T I B = B^T B Substituting the given matrix B , we get: XY = bmatrix 1 & 0 & 1 bmatrix bmatrix 1 0 1 bmatrix XY = [1 1 + 0 0 + 1 1] = [2] Answer: [2]