Matrices & Determinants

Formulas are organized based on their importance in the CAT exam.
1 Properties of Determinants
2 Inverse of a Power
3 Cayley-Hamilton Theorem
4 Fundamental Adjoint Identity
5 Matrix Multiplication
6 Trace of a Product
7 Adjoint of a Matrix
8 Orthogonal Matrix
9 Eigenvalues and Eigenvectors
10 Determinant with a Row Equal to a Sum
11 Adjoint of a Matrix
12 Singular Matrix
13 Matrix Multiplication
14 Powers of a Matrix
15 Inverse of a Matrix
16 Determinant of 3x3 Matrix
17 Scalar Multiplication
18 Trace of a Matrix
19 Lower Triangular Matrix
20 Identity Matrix
21 Minor of an Element
22 Scalar Matrix
23 Addition of Matrices
24 Matrix
25 Solving Matrix Equation $XA=B$
26 Determinant of a $$3\times3$$ Matrix
27 Non-Commutativity of Matrix Multiplication
28 Inverse of a Scalar Multiple
29 Associative Property of Matrix Multiplication
30 Zero Matrix
31 Singular Matrix
32 Distributive Properties of Matrix Multiplication
33 Properties of Matrix Addition
34 Determinant of the Identity Matrix
35 Uniqueness of Inverse
36 Inverse of a Matrix
37 Determinant of a Diagonal Matrix
38 Multiplying a Column by a Scalar
39 Adding a Multiple of One Row to Another
40 Determinant and Transpose
41 Determinant of a Power
42 Transpose of a Matrix Product
43 Inverse of a $$2\times2$$ Matrix
44 Inverse of a Product
45 Non-Singular Matrix
46 Trace of a Scalar Multiple
47 Proportional Rows
48 Rectangular Matrix
49 Diagonal Matrix
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