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  • provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise Fill in the blanks question 2

provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise  Fill in the blanks question 2

Answers (1)

Answer: \left | A \right |=0

Hint: Here, we use basic concept of skew symmetric matrix and determinant of matrix

Given: A is 3\times 3 order skew symmetric matrix

Solution: Here, A_{\left [ 3\times 3 \right ]} and A=-A^{T} ( Skew Symmetric )

                So,  A=-A^{T}

                     \left | A \right |=-\left | A^{T} \right |           [Taking determinant both side]

                     \left | A \right |=-\left | A \right |\; \; \; \; \; \; \; \;                \left [ \left | A^{T} \right |=\left | A \right | \right ]

                     \left | A \right |+\left | A \right |=0

                     2\left | A \right |=0

                     \left | A \right |=0

So, here determinant of 3 3\times 3 skew symmetric matrix always be zero.

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