Matrices — ICSE Class 10

Question 1 • 2023 4 Marks

Given matrices A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix} and B = \begin{pmatrix} 1 & 2 \\ -1 & 0 \end{pmatrix} . Find matrix X such that A^2 - 2AB + X = I , where I is the 2 \times 2 identity matrix.

Answer: X = \begin{pmatrix} -1 & 3 \\ -6 & -8 \end{pmatrix}