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Which of the following is/ are TRUE?Determinant evaluated across any row or column is same.Determinant of a Identity matrix () is 1.If all the elements of a row (or column) are zeros, then the value of the determinant is zero.a.1 and 3 onlyb.3 onlyc.All of the aboved.None

Question

Which of the following is/ are TRUE?Determinant evaluated across any row or column is same.Determinant of a Identity matrix () is 1.If all the elements of a row (or column) are zeros, then the value of the determinant is zero.a.1 and 3 onlyb.3 onlyc.All of the aboved.None

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Solution

The correct answer is c. All of the above.

Here's why:

  1. Determinant evaluated across any row or column is same: This is true. The determinant of a matrix remains the same no matter which row or column you use to calculate it. This is a property of determinants.

  2. Determinant of an Identity matrix (I) is 1: This is also true. The determinant of an identity matrix is always 1, regardless of its dimensions.

  3. If all the elements of a row (or column) are zeros, then the value of the determinant is zero: This is true as well. If a matrix has a row or column of all zeros, its determinant is zero. This is another property of determinants.

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