This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find (B^-1A^-1)^-1, we use the property of matrix inverses (XY)^-1 = Y^-1X^-1. Step 1: Apply the inverse property to the given expression. Using the property (XY)^-1 = Y^-1X^-1, we can rewrite the expression: (B^-1A^-1)^-1 = (A^-1)^-1(B^-1)^-1 Step 2: Apply the property of double inverse. We know that (X^-1)^-1 = X. Applying this to our expression: (A^-1)^-1 = A (B^-1)^-1 = B So, the expression simplifies to: (B^-1A^-1)^-1 = AB Step 3: Calculate the product of matrices A and B. Given matrices: A = 2 & 2 \\ -3 & 2 B = 0 & -1 \\ 1 & 0 Now, we multiply A by B: AB = (2)(0) + (2)(1) & (2)(-1) + (2)(0) \\ (-3)(0) + (2)(1) & (-3)(-1) + (2)(0) AB = 0 + 2 & -2 + 0 \\ 0 + 2 & 3 + 0 AB = 2 & -2 \\ 2 & 3 Step 4: Compare the result with the given options. The calculated matrix is 2 & -2 \\ 2 & 3 . This matches option (A). The final answer is A. That's 2 down. 3 left today — send the next one.