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  • Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question 23

Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question23

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Answer: Hence proved, A^2 = l_3

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: A=\left[\begin{array}{ccc}4 & -1 & -4 \\ 3 & 0 & -4 \\ 3 & -1 & -3\end{array}\right]

Prove:A^2 = l_3

As we know, l_3  is identity matrix of size 3

l_3 = =\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]

Consider, A^{2}=A A

A^{2}=\left[\begin{array}{ccc}4 & -1 & -4 \\ 3 & 0 & -4 \\ 3 & -1 & -3\end{array}\right]\left[\begin{array}{ccc}4 & -1 & -4 \\ 3 & 0 & -4 \\ 3 & -1 & -3\end{array}\right]\\\\\\\ =\left[\begin{array}{ccc}16-3-12 & -4+0+4 & -16+4+12 \\ 12+0-12 & -3+0+4 & -12+0+12 \\ 12-3-9 & -3+0+3 & -12+4+9\end{array}\right]\\\\\\ =\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]=I_{3}

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