Five marks exercise problems V — task. Mathematics State Board, Class 10.

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1. If \(A =\)

(\begin{array}{l} \cos θ & 0 \\ 0 & \cos θ \end{array})

, \(B =\)

(\begin{array}{l} \sin θ & 0 \\ 0 & \sin θ \end{array})

then show that \(A^2 + B^2 = I\).

2. If \(A =\)

(\begin{array}{l} a & b \\ c & d \end{array})

and \(I =\)

(\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array})

show that \(A^2 - (a + d)A = (Bc - ad) I_2\).

Important!

This is a self-assessment task. Solve this question and assess the solution steps after completing the exercise.

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9. Five marks exercise problems V