Question:

Given: Problem statement: If $A = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}, B = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}, C = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, find matrix $D$ such that $CD - AB = O$.
Step 1: Set up matrix algebraic expressions:
Compute intermediate powers ($A^2, A^3$) or matrix operations accurately. [1.0 Mark]
Step 2: Execute matrix products and reductions:
Substitute matrices into left-hand side expression. [1.0 Mark]
Step 3: Evaluate final matrix / verify equality:
Show that resultant matrix simplifies to target matrix/zero matrix. [1.0 Mark]
Conclusion: Required matrix equality proved.

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🎯 Official CBSE Marking Scheme:
Evaluating matrix powers/products: 1.0 Mark
Substituting into matrix polynomial: 1.0 Mark
Simplifying to final zero/identity matrix: 1.0 Mark