# How do you find the det of a matrix

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## What is det A in matrix?

In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. … The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one).

**The determinant of a matrix A**is denoted det(A), det A, or |A|.## How do you find the det of a 2×2 matrix?

In other words, to take the determinant of a 2×2 matrix, you

**multiply the top-left-to-bottom-right diagonal**, and from this you subtract the product of bottom-left-to-top-right diagonal.## How do you find the DET of a 3×3 matrix?

## How do you find the DET of a 4×4 matrix?

## How do you find Det 2A?

Thus det(kA) = (k^n)×det(A), where n is the number of rows(or columns) of A. Therefore if it is an n×n matrix A, then the determinant of the matrix 2A is

**(2^n)×det(A) = (2^n)×4**.## What is det A 1?

The determinant of the inverse of an invertible matrix is the inverse of the determinant:

**det(A**[6.2. 6, page 265]. Similar matrices have the same determinant; that is, if S is invertible and of the same size as A then det(S A S^{–}^{1}) = 1 / det(A)^{–}^{1}) = det(A).## How do you find the 2 of a 3×3 matrix?

## How do you find det AB?

If A and B are n × n matrices, then

**det(AB) = (detA)(detB)**. In other words, the determinant of a product of two matrices is just the product of the deter- minants.## How do you find Det A N?

It maps a matrix of numbers to a number in such a way that for two matrices A,B , det(AB)=det(A)det(B) . and so on. Therefore in general

**det(An)=det(A)n for any n∈**N .## How do you find det B from Det A?

Let B be the result of adding to a row in A a multiple of another row in A. Then,

**det(B) = det(A)**. Let B be the result of interchanging two rows in A. Then, det(B) = − det(A).## Is detA B detA det B )?

Therefore det(A) and

**det(B) are both zero**and hence det(A)+det(B)=0+0=0 holds. What we have proved essentially is that if if AB=O, for square matrices A and B, then det(A)=0=det(B), from which the result follows.## Is detA detA T?

Originally Answered: Is it true that det(a) = -det(A) = det(A^T)? det(a) is of course

**in general not -det(A) unless the determinant is zero**. But indeed the determinant of a matrix is that of its transposed matrix (mirror-ed at the diagonal), if that is what your notation is supposed to denote.## Is detA det (- A?

det(-A) = -det(A) for

**Odd Square Matrix**In words: the negative determinant of an odd square matrix is the determinant of the negative matrix.

## What is det cA?

Successful at helping students improve in math! The answer is that, if A is a square matrix of order n×n,

**det(cA) = c**. To prove this, remember that multiplying any row or column of a square matrix by a constant c will change the determinant by a factor of c.^{n}det(A)## Is Det A det at?

Attempted solution: If

**detA=0**, the A is non-invertible. We know that a matrix is invertible iff At is invertible. As A is non-invertible, so is At and therefore detAt=0.## What is det B5?

Since the determinant is multiplicative,

**det B5 = (det B)5 = (−2)5 = −32**. of polynomials.## Why is the determinant of a skew symmetric matrix 0?

Determinant of Skew-Symmetric Matrix is equal to Zero

**if its order is odd**. It is one of the property of skew symmetric matrix. If, we have any skew-symmetric matrix with odd order then we can directly write its determinant equal to zero. We can verify this property using an example of skew-symmetric 3×3 matrix.Ads by Google