Adjoint and Inverse of a Matrix

IMPORTANT

Adjoint and Inverse of a Matrix: Overview

This topic covers concepts, such as, Singular and Non-singular Matrices, Adjoint of a Matrix, Cofactor Matrix, Properties of Adjoint of Matrices & Inverse of a Matrix Using Adjoint etc.

Important Questions on Adjoint and Inverse of a Matrix

HARD
IMPORTANT

Using matrix method, the solution of the following system of linear equations would be :

  x+yz=1 xyz=1 3x+y2z=3

MEDIUM
IMPORTANT

Using properties of determinants, the value of

  | b+c a a b c+a b c c a+b |  would be:

EASY
IMPORTANT

Let A, B, C be three 4×4 matrices such that detA=5,detB=-3, and detC=12. Then the det2AB-1C3BT is

MEDIUM
IMPORTANT

Let P be a matrix of order 3×3 and det(P)=3, then the value of detadjadj P is

EASY
IMPORTANT

For any 2×2 matrix, if Aadj A=200020, then A equals

MEDIUM
IMPORTANT

If Q is a non-singular matrix, then the value of adj(Q-1) in terms of Q is

MEDIUM
IMPORTANT

If the value of a third order determinant is 10, then the value of the square of the determinant formed by its cofactors will be

HARD
IMPORTANT

If A=123012001 and BA=A, where B represent 3×3 order matrix. If total number of 1's in matrix A-1 and matrix B are p and q respectively, then the value of p2+q2 is

MEDIUM
IMPORTANT

If A=-241-3, then A-1=.

MEDIUM
IMPORTANT

If A=2    3    13    4    13    7    2, then adjA=

MEDIUM
IMPORTANT

If A=3-342-340-11, then adj(adjA) is

MEDIUM
IMPORTANT

If P=1x013024-2 is the adjoint of 3×3 matrix A and A=4, then x is

MEDIUM
IMPORTANT

If A=2015 and B=1420, then adjAB=

HARD
IMPORTANT

If A=7342, then 9I2-A=

MEDIUM
IMPORTANT

If A=3512, B=adjA and C=3A, then |adjB||C|=

MEDIUM
IMPORTANT

If |adj(adjA)|=|A|9, then the order of the square matrix is

HARD
IMPORTANT

Let A be a matrix of order 3×3 such that detA=2, B=2A-1and C=(adjA)163 , then the value of detA3B2C3 is

EASY
IMPORTANT

If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 

EASY
IMPORTANT

The adjoint of the matrix A=2-335 is

MEDIUM
IMPORTANT

If A=k2000l3000m4 and A-1=120001300014 then k+l+m=