Question

Let \(A = \begin{bmatrix} 3 & 5\\ -2 & -3 \end{bmatrix}\). If \(BA^2 = A\), where \(B\) is a \(2 \times 2\) matrix, then \(B = \)

• A. \(\begin{bmatrix} -3 & -5\\ 2 & 3 \end{bmatrix}\)
• B. \(\begin{bmatrix} 3 & -5 \\ 2 & -3 \end{bmatrix}\)
• C. \(\begin{bmatrix} 3 & -2 \\ 5 & -3 \end{bmatrix}\)
• D. \(\begin{bmatrix} 3 & 2 \\ -5 & -3 \end{bmatrix}\)
• E. \(\begin{bmatrix} 3 & 5 \\ -2 & -3 \end{bmatrix}\)

Hint:

To find the inverse of a \(2 \times 2\) matrix quickly: swap the diagonal elements, change the signs of the off-diagonal elements, and divide by the determinant.

Answer 1

The Correct Option is A