Question

Which of the following statements are true?

If any row of a square matrix is zero, its determinant is zero.

If all numbers in a matrix are equal, its determinant is zero.

The determinant of any identity matrix is zero.

The determinant of a matrix with all positive numbers is always positive.

The determinant of any zero matrix is zero

Answer 1

Answer:

1,2,5

Step-by-step explanation:

Answer 2

The 3 statements given below are true.

Any row of a square matrix is zero, its determinant is zero.

All numbers in a matrix are equal, its determinant is zero.

The determinant of any zero matrix is zero.

What is matrix?

It is an arrangement of elements, especially numbers, in a particular way. A matrix is a mathematical structure having rows and columns. The element aij of a matrix, say M refers to the element in the i-th row and j-th column.

If any row of a square matrix is zero, its determinant is zero, because the entire line makes the determinant zero.

If all numbers in a matrix are equal, its determinant is zero, because calculation makes zero in each term.

The determinant of any zero matrix is zero, because calculation of zero gives zero as a result.

Hence,

Any row of a square matrix is zero, its determinant is zero.

All numbers in a matrix are equal, its determinant is zero.

The determinant of any zero matrix is zero.

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