DETERMINANTS

If we interchange any two rows (or columns), then sign of determinant .

If any two rows or any two columns are identical or proportional, then value of determinant is .

If we multiply each element of a row or a column of a determinant by constant k, then value of determinant is .

Multiplying a determinant by k means elements of only one row (or one column) by k.

Value of of a matrix A is obtained by sum of product of elements of a row (or a column) with corresponding cofactors.

If elements of one row (or column) are multiplied with cofactors of elements of any other row (or column), then their sum is .

A (adj A) = = |A| I.

If AB = BA = I, where B is matrix, then B is called of A.

A square matrix A has inverse if and only if A is .

A system of equation is consistent or inconsistent according as its exists or not.

For a square matrix A in matrix equation AX = B, |A| = 0 and (adj A) B ≠ 0, then there exists

For a square matrix A in matrix equation AX = B, |A| ≠ 0, there exists .

For a square matrix A in matrix equation AX = B, |A| = 0 and (adj A) B = 0, then system may or may not be .

Only matrices have determinants.

The value of the determinant remains if its rows and columns are interchanged.

If any two rows (or columns) of a determinant are interchanged, then sign of determinant .

If any two rows (or columns) of a determinant are identical, then value of determinant is .

The adjoint of a square matrix is defined as the of the matrix.

A square matrix A is said to be if A = 0.

A square matrix A is said to be if A ≠ 0.

If A and B are nonsingular matrices of the same order, then AB and BA are matrices of the same order.

A square matrix A is if and only if A is nonsingular matrix.

A system of equations is said to be if its solution (one or more) exists

A system of equations is said to be if its solution does not exist.

DETERMINANTS

Gap-fill exercise