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#### Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 5 sub question (iii)

$\begin{bmatrix} 0 &-1 &1 \\ 2& 0 &-2 \\ 5& -2 &-3 \end{bmatrix}$

Hint: A matrix can be multiplied by any other matrix that has the same number of rows as the first has columns.

Given: $\left[\begin{array}{cc} 1 & -1 \\ 0 & 2 \\ 2 & 3 \end{array}\right]\left(\left[\begin{array}{lll} 1 & 0 & 2 \\ 2 & 0 & 1 \end{array}\right]-\left[\begin{array}{lll} 0 & 1 & 2 \\ 1 & 0 & 2 \end{array}\right]\right)$

Firstly, we have to subtract the matrix which is inside brackets,

\begin{aligned} &=\left[\begin{array}{cc} 1 & -1 \\ 0 & 2 \\ 2 & 3 \end{array}\right]\left[\begin{array}{ccc} 1-0 & 0-1 & 2-2 \\ 2-1 & 0-0 & 1-2 \end{array}\right] \\ &=\left[\begin{array}{cc} 1 & -1 \\ 0 & 2 \\ 2 & 3 \end{array}\right]\left[\begin{array}{ccc} 1 & -1 & 0 \\ 1 & 0 & -1 \end{array}\right] \end{aligned}

\begin{aligned} &=\left[\begin{array}{ccc} 1 \times 1+(-1) \times 1 & 1 \times(-1)+(-1) \times 0 & 1 \times 0+(-1) \times(-1) \\ 0 \times 1+2 \times 1 & 0 \times(-1)+2 \times 0 & 0 \times 0+2 \times(-1) \\ 2 \times 1+3 \times 1 & 2 \times(-1)+3 \times 0 & 2 \times 0+3 \times(-1) \end{array}\right] \\ &=\left[\begin{array}{ccc} 1-1 & -1+0 & 0+1 \\ 0+2 & 0+0 & 0-2 \\ 2+3 & -2+0 & 0-3 \end{array}\right] \end{aligned}

$=\begin{bmatrix} 0 &-1 &1 \\ 2& 0 &-2 \\ 5& -2 &-3 \end{bmatrix}$