Matrices & Determinants

Formulas are organized based on their importance in the CAT exam.
1 Inverse of a Power
2 Orthogonal Matrix
3 Fundamental Adjoint Identity
4 Determinant with a Row Equal to a Sum
5 Adjoint of a Matrix
6 Eigenvalues and Eigenvectors
7 Cayley-Hamilton Theorem
8 Adjoint of a Matrix
9 Trace of a Product
10 Properties of Determinants
11 Powers of a Matrix
12 Inverse of a Matrix
13 Singular Matrix
14 Matrix Multiplication
15 Determinant of 3x3 Matrix
16 Lower Triangular Matrix
17 Scalar Multiplication
18 Addition of Matrices
19 Identity Matrix
20 Trace of a Matrix
21 Minor of an Element
22 Scalar Matrix
23 Matrix
24 Non-Commutativity of Matrix Multiplication
25 Associative Property of Matrix Multiplication
26 Solving Matrix Equation $XA=B$
27 Determinant of a $$3\times3$$ Matrix
28 Inverse of a Scalar Multiple
29 Zero Matrix
30 Singular Matrix
31 Distributive Properties of Matrix Multiplication
32 Determinant and Transpose
33 Transpose of a Matrix Product
34 Properties of Matrix Addition
35 Determinant of the Identity Matrix
36 Uniqueness of Inverse
37 Inverse of a Matrix
38 Determinant of a Diagonal Matrix
39 Multiplying a Column by a Scalar
40 Adding a Multiple of One Row to Another
41 Determinant of a Power
42 Proportional Rows
43 Inverse of a $$2\times2$$ Matrix
44 Inverse of a Product
45 Non-Singular Matrix
46 Trace of a Scalar Multiple
47 Rectangular Matrix
48 Diagonal Matrix
49 Matrix Multiplication
50 Adding a Multiple of One Column to Another
51 Proportional Columns
52 Expansion of a Determinant Along a Row
53 Solving Matrix Equation $$AX=B$$
54 Transpose of a Matrix
55 Decomposition into Symmetric and Skew-Symmetric Matrices
56 Properties of Scalar Multiplication
57 Row Matrix
58 Subtraction of Matrices
59 Expansion of a Determinant Along a Column
60 Effect of Interchanging Two Columns
61 Cofactor of an Element
62 Solving $AXB=C$
63 Cancellation Using Inverse
64 Matrix Polynomial
65 Determinant of the Adjoint
66 Condition for Inverse Existence
67 Determinant of a Matrix Equation
68 Symmetric Matrix
69 Skew-Symmetric Matrix
70 Determinant of 2x2 Matrix
71 Equality of Matrices
72 Transpose of Matrix Powers
73 Two Identical Columns
74 Sum of Determinants
75 Identity Matrix in Multiplication
76 Effect of Interchanging Two Rows
77 Matrix Equation Solution
78 Square Matrix
79 Determinant of a $$2\times2$$ Matrix
80 Cayley-Hamilton Theorem
81 Inverse of Transpose
82 Determinant of a Zero Matrix
83 Properties of Transpose
84 Determinant of an Inverse
85 Scalar Multiplication
86 Adjoint of a Scalar Multiple
87 Two Identical Rows
88 Order of a Matrix
89 Common Factor from a Row
90 Column Matrix
91 Determinant of a Triangular Matrix
92 Determinant of a Product
93 Trace of a Sum
94 Adjoint of a Product
95 Adjoint of a Transpose
96 Zero Matrix in Multiplication
97 Upper Triangular Matrix
98 Inverse of an Inverse
99 Determinant of a Scalar Multiple
100 Matrix Addition
101 Transpose of a Matrix
102 Inverse Using Adjoint
103 Common Factor from a Column
104 Multiplying a Row by a Scalar
105 Matrix Definition and Order