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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