78992
If \(M\) is any square matrix of order 3 over \(R\) and if \(M^{\prime}\) be the transpose of \(M\), then adj \(\left(M^{\prime}\right)\) \((\operatorname{adj} \mathbf{M})^{\prime}\) is equal to
78961
Inverse of a diagonal non-singular matrix is
1 diagonal matrix
2 scalar matrix
3 skew symmetric matrix
4 zero matrix
Explanation:
(A) : A diagonal matrix has element only in its diagonal. So, the inverse is also having all the non-zero elements in the diagonal. So, it will be symmetric and will also be a diagonal matrix.
Karnataka CET-2012
Matrix and Determinant
78987
If \(A\) is an invertible matrix of order \(n\), then the determinant of adj (A) is equal to
1 \(|\mathrm{A}|^{\mathrm{n}}\)
2 \(|A|^{n+1}\)
3 \(|\mathrm{A}|^{\mathrm{n}-1}\)
4 \(|\mathrm{A}|^{\mathrm{n}+2}\)
Explanation:
(C): Since, \(\mathrm{A}\) is an invertible matrix of order \(\mathrm{n}\), then the determinant of \(\operatorname{adj}(A)=|A|^{n-1}\).
78992
If \(M\) is any square matrix of order 3 over \(R\) and if \(M^{\prime}\) be the transpose of \(M\), then adj \(\left(M^{\prime}\right)\) \((\operatorname{adj} \mathbf{M})^{\prime}\) is equal to
78961
Inverse of a diagonal non-singular matrix is
1 diagonal matrix
2 scalar matrix
3 skew symmetric matrix
4 zero matrix
Explanation:
(A) : A diagonal matrix has element only in its diagonal. So, the inverse is also having all the non-zero elements in the diagonal. So, it will be symmetric and will also be a diagonal matrix.
Karnataka CET-2012
Matrix and Determinant
78987
If \(A\) is an invertible matrix of order \(n\), then the determinant of adj (A) is equal to
1 \(|\mathrm{A}|^{\mathrm{n}}\)
2 \(|A|^{n+1}\)
3 \(|\mathrm{A}|^{\mathrm{n}-1}\)
4 \(|\mathrm{A}|^{\mathrm{n}+2}\)
Explanation:
(C): Since, \(\mathrm{A}\) is an invertible matrix of order \(\mathrm{n}\), then the determinant of \(\operatorname{adj}(A)=|A|^{n-1}\).
78992
If \(M\) is any square matrix of order 3 over \(R\) and if \(M^{\prime}\) be the transpose of \(M\), then adj \(\left(M^{\prime}\right)\) \((\operatorname{adj} \mathbf{M})^{\prime}\) is equal to
78961
Inverse of a diagonal non-singular matrix is
1 diagonal matrix
2 scalar matrix
3 skew symmetric matrix
4 zero matrix
Explanation:
(A) : A diagonal matrix has element only in its diagonal. So, the inverse is also having all the non-zero elements in the diagonal. So, it will be symmetric and will also be a diagonal matrix.
Karnataka CET-2012
Matrix and Determinant
78987
If \(A\) is an invertible matrix of order \(n\), then the determinant of adj (A) is equal to
1 \(|\mathrm{A}|^{\mathrm{n}}\)
2 \(|A|^{n+1}\)
3 \(|\mathrm{A}|^{\mathrm{n}-1}\)
4 \(|\mathrm{A}|^{\mathrm{n}+2}\)
Explanation:
(C): Since, \(\mathrm{A}\) is an invertible matrix of order \(\mathrm{n}\), then the determinant of \(\operatorname{adj}(A)=|A|^{n-1}\).
