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Please solve RD Sharma class 12 Chapter Algebra of Matrices  exercise 4.3 question 1 sub question (i) maths textbook solution.

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\begin{bmatrix} a^2 +b^2 &0 \\ 0 & a^2 +b^2 \end{bmatrix}

Hint: matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: ab-baa-bba\begin{bmatrix} a &b \\ -b & a \end{bmatrix} \begin{bmatrix} a &-b \\ b &a \end{bmatrix}

\begin{aligned} &=\left[\begin{array}{cc} a \times a+b \times b & a \times(-b)+b \times a \\ (-b) \times a+a \times b & (-b) \times(-b)+a \times a \end{array}\right] \\ &=\left[\begin{array}{cc} a^{2}+b^{2} & -a b+b a \\ -a b+a b & b^{2}+a^{2} \end{array}\right] \end{aligned}

On simplification we get,

\begin{bmatrix} a^2+b^2 &0 \\ 0 &b^2+a^2 \end{bmatrix}

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