In this video, we will get to learn about the area of a triangle and will also learn to solve a determinant using some properties without expanding it.

• Three points would be collinear; if the area of the triangle formed by these three points as vertices is zero.

• Some properties that can be used to solve a determinant without expanding it are:

a) If, to each element of any row or column of a determinant, the corresponding elements of another row (or column) are added, then the value of determinant remains the same

b) Also, if, from each element of any row or column of a determinant, the corresponding elements of another row (or column) are subtracted, then the value of determinant remains the same

c) If any two rows or any two columns of a determinant are identical, or proportional, then the value of the determinant is zero

• If elements of a row or a column in a determinant can be expressed as the sum of two or more elements, then the given determinant can be expressed as the sum of two or more determinants.