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(A) Given matrices are $A = \begin{bmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ -3 & 2 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \ -2 & 1 & 0 \ 7

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$I$

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(A) Given matrices are $A = \begin{bmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ -3 & 2 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \ -2 & 1 & 0 \ 7 & -2 & 1 \end{bmatrix}$.To find $AB$,we perform matrix multiplication:$AB = \begin{bmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ -3 & 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 \ -2 & 1 & 0 \ 7 & -2 & 1 \end{bmatrix}$Calculating each element:Row $1$: $(1)(1) + (0)(-2) + (0)(7) = 1$,$(1)(0) + (0)(1) + (0)(-2) = 0$,$(1)(0) + (0)(0) + (0)(1) = 0$Row $2$: $(2)(1) + (1)(-2) + (0)(7) = 2 - 2 = 0$,$(2)(0) + (1)(1) + (0)(-2) = 1$,$(2)(0) + (1)(0) + (0)(1) = 0$Row $3$: $(-3)(1) + (2)(-2) + (1)(7) = -3 - 4 + 7 = 0$,$(-3)(0) + (2)(1) + (1)(-2) = 2 - 2 = 0$,$(-3)(0) + (2)(0) + (1)(1) = 1$Thus,$AB = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix} = I$.

If $A = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ -3 & 2 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 7 & -2 & 1 \end{bmatrix}$,then $AB$ equals

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